Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Algebra
For the following exercises, match each function in Figure 17 with the letter corresponding to its graph. d(x)=log(x)For the following exercises, match each function in Figure 17 with the letter corresponding to its graph. f(x)=ln(x)For the following exercises, match each function in Figure 17 with the letter corresponding to its graph. g(x)=log2(x)For the following exercises, match each function in Figure 17 with the letter corresponding to its graph. h(x)=log5(x)For the following exercises, match each function in Figure 17 with the letter corresponding to its graph. j(x)=log25(x)For the following exercises, match each function in Figure 18 with the letter corresponding to its graph. 32.For the following exercises, match each function in Figure 18 with the letter corresponding to its graph. f(x)=log13(x)For the following exercises, match each function in Figure 18 with the letter corresponding to its graph. g(x)=log2(x)For the following exercises, match each function in Figure 18 with the letter corresponding to its graph. h(x)=log34(x)For the following exercises, sketch the graphs of each pair of functions on the same axis. f(x)=log(x) and g(x)=10xFor the following exercises, sketch the graphs of each pair of functions on the same axis. f(x)=log(x) and g(x)=log12(x)For the following exercises, sketch the graphs of each pair of functions on the same axis. f(x)=log4(x) and g(x)=ln(x)For the following exercises, sketch the graphs of each pair of functions on the same axis. f(x)=ex and g(x)=ln(x)For the following exercises, match each function in Figure 19 with the letter corresponding to its graph. f(x)=log4(x+2)For the following exercises, match each function in Figure 19 with the letter corresponding to its graph. g(x)=log4(x+2)For the following exercises, match each function in Figure 19 with the letter corresponding to its graph. h(x)=log4(x+2)For the following exercises, sketch the graph of the indicated function. f(x)=log2(x+2)For the following exercises, sketch the graph of the indicated function. f(x)=2log(x)For the following exercises, sketch the graph of the indicated function. f(x)=ln(x)For the following exercises, sketch the graph of the indicated function. g(x)=log(4x+16)+4For the following exercises, sketch the graph of the indicated function. g(x)=log(63x)+1For the following exercises, sketch the graph of the indicated function. h(x)=12ln(x+1)3For the following exercises, write a logarithmic equation corresponding to the graph shown. Use y=log2(x) as the parent function.For the following exercises, write a logarithmic equation corresponding to the graph shown. Use f(x)=log3(x) as the parent function.For the following exercises, write a logarithmic equation corresponding to the graph shown. Use f(x)=log4(x) as the parent function.For the following exercises, write a logarithmic equation corresponding to the graph shown. Use f(x)=log5(x) as the parent function.For the following exercises, use a graphing calculator to find approximate solutions to each equation. log(x1)+2=ln(x1)+2For the following exercises, use a graphing calculator to find approximate solutions to each equation. log(2x3)+2=log(2x3)+5For the following exercises, use a graphing calculator to find approximate solutions to each equation. ln(x2)=ln(x+1)For the following exercises, use a graphing calculator to find approximate solutions to each equation. 2ln(5x+1)=12ln(5x)+1For the following exercises, use a graphing calculator to find approximate solutions to each equation. 13log(1x)=log(x+1)+13Let b be any positive real number such that b1. What must logb1 be equal to? Verify the result.Explore and discuss the graphs of f(x)=log12(x) and g(x)=log2(x). Make a conjecture based onthe result.Prove the conjecture made in the previous exercise.What is the domain of the function f(x)=ln(x+2x4) ? Discuss the result.Use properties of exponents to find the x-interceptsofthe function f(x)=log(x2+4x+4) algebraically. Show the steps for solving, and then verify the resultby graphing the function.Expand logb(8k).Expand log3(7x2+21x7x(x1)(x2)).Expand ln(x2).Expand ln(1x2).Rewrite 2log3(4) using the power rule for logs to a single logarithm with a leading coefficient of 1.Expand log(x2y3z4).Expand ln(x23) .Expand ln((x1)(2x+1)2x29)Condense log(3)log(4)+log(5)log(6).Rewrite log(5)+0.5log(x)log(7x1)+3log(x1) as a single logarithm.Condense 4(3log(x)+log(x+5)log(2x+3)).How does the pH change when the concentration of positive hydrogen ions is decreased by half?Change log0.5(8) to a quotient of natural logarithms.Evaluate log5(100) using the change-of-base formula.How does the power rule for logarithm help whensolving logarithms with the form logb(xn) ?What does the change-of-base formula do? Whyis ituseful when using a calculator?For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. logb(7x2y)For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. ln(3ab5c)For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. logb(1317)For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log4(xzw)For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. ln(14k)For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log2(yx)For the following exercises, condense to a single logarithm if possible. ln(7)+ln(x)+ln(y)For the following exercises, condense to a single logarithm if possible. log3(2)+log3(a)+log3(11)+log3(b)For the following exercises, condense to a single logarithm if possible. logb(28)logb(7)For the following exercises, condense to a single logarithm if possible. ln(a)ln(d)ln(c)For the following exercises, condense to a single logarithm if possible. logb(17)For the following exercises, condense to a single logarithm if possible. 13ln(8)For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log(x 15y 13z 19)For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. ln(a 2b 4c5)For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log(x3y 4)For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. ln(yy 1y)For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log(x2y3x2y53)For the following exercises, condense each expression to a single logarithm using the properties of logarithms. log(2x4)+log(3x5)For the following exercises, condense each expression to a single logarithm using the properties of logarithms. ln(6x9)ln(3x2)For the following exercises, condense each expression to a single logarithm using the properties of logarithms. 2log(x)+3log(x+1)For the following exercises, condense each expression to a single logarithm using the properties of logarithms. log(x)12log(y)+3log(z)For the following exercises, condense each expression to a single logarithm using the properties of logarithms. 4log7(c)+log7(a)3+log7(b)3For the following exercises, rewrite each expression as an equivalent ratio of logs using the indicated base. 25. log7(15) to base eFor the following exercises, rewrite each expression as an equivalent ratio of logs using the indicated base. log14(55.875) to base 10For the following exercises, suppose log5(6)=a and log5(11)=b. Use the change-of-base formula along with properties of logarithm to rewrite each expression in terms of a and b. Show the steps for solving. log11(5)For the following exercises, suppose log5(6)=a and log5(11)=b. Use the change-of-base formula along with properties of logarithm to rewrite each expression in terms of a and b. Show the steps for solving. log6(55)For the following exercises, suppose log5(6)=a and log5(11)=b. Use the change-of-base formula along with properties of logarithm to rewrite each expression in terms of a and b. Show the steps for solving. 29. log11(611)For the following exercises, use properties of logarithm to evaluate without using a calculator. 30. log3(19)3log3(3)For the following exercises, use properties of logarithms to evaluate without using a calculator. 6log8(2)+log8(64)3log8(4)For the following exercises, use properties of logarithms to evaluate without using a calculator. 2log9(3)4log9(3)+log9(1729)For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to ?ve decimal places. log3(22)For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to ?ve decimal places. log8(65)For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to ?ve decimal places. log6(5.38)For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to ?ve decimal places. log4(152)For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to ?ve decimal places. log12(4.7)Use the product rule for logarithms to find all xvalues such that log12(2x+6)+log12(x+2)=2. Show the steps for solving.Use the quotient rule for logarithms to find all xvalues such that log6(x+2)log6(x3)=1. Showthe steps for solving.Can the power property oflogarithms be derivedfrom the power property of exponents using theequation bx=m ?If not, explain why. If so, show thederivation.Prove that logb(n)=1logn(b) for any positive integers b1 and n1.Does log81(2401)=log3(7) ? Verify the claimalgebraically.Solve 52x=53x+2.Solve 52x=253x+2.Solve 5x=5.Solve 2x=100.Solve 2x=3x+1.Solve 3e0.5t=11.Solve 3+e2t=7e2t.Solve e2x=ex+2.Solve 6+ln(x)=10.Solve 2ln(x+1)=10.Use a graphing calculator to estimate the approximate solution to the logarithmic equation 2x=1000 to 2 decimalplaces.Solve ln(x2)=ln(1).How long will it take before twenty percent of our 1,000 -gram sample of uranium- 235 has decayed?How can an exponential equation be solved?When does an extraneous solution occur? How canan extraneous solution be recognized?When can the one-to-one property oflogarithms beused to solve an equation? When can it not be used?For the following exercises, use like bases to solve the exponential equation. 43v2=4vFor the following exercises, use like bases to solve the exponential equation. 6443x=16For the following exercises, use like bases to solve the exponential equation. 32x+13x=243For the following exercises, use like bases to solve the exponential equation. 7. 23n14=2n+2For the following exercises, use like bases to solve the exponential equation. 62553x+3=125For the following exercises, use like bases to solve the exponential equation. 363b362b=2162bFor the following exercises, use like bases to solve the exponential equation. 10. (164)3n8=26For the following exercises, use logarithms to solve. 9x10=1For the following exercises, use logarithms to solve. 2e6x=13For the following exercises, use logarithms to solve. er+1010=42For the following exercises, use logarithms to solve. 2109a=29For the following exercises, use logarithms to solve. 810p+77=24For the following exercises, use logarithms to solve. 7e3n5+5=89For the following exercises, use logarithms to solve. e3k+6=44For the fo?awing exercises, use logarithms to solve. 5e9x88=62For the following exercises, use logarithms to solve. 6e9x+8+2=74For the following exercises, use logarithms to solve. 2x+1=52x1For the following exercises, use logarithms to solve. e2xex132=0For the following exercises, use logarithms to solve. 7e8x+85=95For the following exercises, use logarithms to solve. 23. 10e8x+3+2=8For the following exercises, use logarithms to solve. 24. 4e3x+37=53For the following exercises, use logarithms to solve. 8e5x24=90For the following exercises, use logarithms to solve. 32x+1=7x2For the following exercises, use logarithms to solve. e2xex6=0For the following exercises, use logarithms to solve. 3e33x+6=31For the following exercises, use the definition of a logarithm to rewrite the equation as an exponential equation. log(1100)=2For the following exercises, use the definition of a logarithm to rewrite the equation as an exponential equation. log324(18)=12For the following exercises, use the definition of a logarithm to solve the equation. 5log7(n)=10For the following exercises, use the definition of a logarithm to solve the equation. 8log9(x)=16For the following exercises, use the definition of a logarithm to solve the equation. 4+log2(9k)=2For the following exercises, use the definition of a logarithm to solve the equation. 2log(8n+4)+6=10For the following exercises, use the definition of a logarithm to solve the equation. 104ln(98x)=6For the following exercises, use the one-to-one property of logarithms to solve. ln(103x)=ln(4x)For the following exercises, use the one-to-one property of logarithms to solve. log13(5n2)=log13(85n)For the following exercises, use the one-to-one property of logarithms to solve. log(x+3)log(x)=log(74)For the following exercises, use the one-to-one property of logarithms to solve. ln(3x)=ln(x26x)For the following exercises, use the one-to-one property of logarithms to solve. log4(6m)=log43(m)For the following exercises, use the one-to-one property of logarithms to solve. ln(x2)ln(x)=ln(54)For the following exercises, use the one-to-one property of logarithms to solve. log9(2n214n)=log9(45+n2)For the following exercises, use the one-to-one property of logarithms to solve. ln(x210)+ln(9)=ln(10)For the following exercises, solve each equation for x . log(x+12)=log(x)+log(12)For the following exercises, solve each equation for x . ln(x)+ln(x3)=ln(7x)For the following exercises, solve each equation for x . log2(7x+6)=3For the following exercises, solve each equation for x . ln(7)+ln(24x2)=ln(14)For the following exercises, solve each equation for x . 48. log8(x+6)log8(x)=log8(58)For the following exercises, solve each equation for x . 49. ln(3)ln(33x)=ln(4)For the following exercises, solve each equation for x. 50. log3(3x)log3(6)=log3(77)For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. 51. log9(x)5=4For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. 52. log3(x)+3=2For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. 53. ln(3x)=2For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. 54. ln(x5)=1For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. log(4)+log(5x)=2For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. 7+log3(4x)=6For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. ln(4x10)6=5For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution log(42x)=log(4x)For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. log11(2x27x)=log11(x2)For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. ln(2x+9)=ln(5x)For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. log9(3x)=log9(4x8)For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. log(x2+13)=log(7x+3)For the following exercises, solve the equation for x , if there is a solution. Than graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. 3log2(10)log(x9)=log(44)For the following exercises, solve the equation for x, if there is a solution. Than graph both sides of the equation, andobserve the point of intersection (if it exists) to verify the solution. 64. ln(x)ln(x+3)=ln(6)For the following exercises, solve for the indicated value, and graph the situation showing the solution point. An account with an initial deposit of 6,500 earns 7.25 annual interest, compounded continuously. How much will the account be worth after 20 years?For the following exercises, solve for the indicated value, and graph the situation showing the solution point. The formula for measuring sound intensity in decibels D is defined by the equation D=10log(II0), where I is the intensity of the sound in watts per square meter and I0=1012 is the lowest level of sound that the average person can hear. How many decibels are emitted from a jet plane with a sound intensity of 8.3102 watts per square meter?For the following exercises, solve for the indicated value, and graph the situation showing the solution point. The population of a small town is modeled by the equation P=1650e0.5t where t is measured in years. In approximately how many years will the town's population reach 20,000 ?For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places. 1000(1.03)t=5000 using the common log.For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places. e5x=17 using the natural logFor the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places. 3(1.04)3t=8 using the common logFor the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places. 34x5=38 using the common logFor the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places. 50e0.12t=10 using the natural logFor the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth. 7e3x5+7.9=47For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth. ln(3)+ln(4.4x+6.8)=2For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth. log(0.7x9)=1+5log(5)For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth. Atmospheric pressure P in pounds per square inch is represented by the formula P=14.7e0.21x , where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.369 pounds per square inch? (Hint: there are 5280 feet in a mile)For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth. The magnitude M of an earthquake is represented by the equation M=23log(EE0) where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. To the nearest hundredth what would the magnitude be of an earthquake releasing 1.41013 joules of energy?Use the definition of a logarithm along with the one-to-one property oflogarithms to prove that blogbx=x.Recall the formula for continually compoundinginterest, y=Aekt. Use the definition of a logarithmalong with Properties of logarithms to solve theformula for time t such that tis equal to a singlelogarithm.Recall the compound interest formula A=a(1+rk)kt. Use the definition of a logarithm along withproperties of logarithms to solve the formula for time t.Newton’s Law ofCooling states that the temperatureTof an object at any time t can be described by theequation T=Ts+(T0Ts)ekt, where Ts is thetemperature of the surrounding environment, T0 is the initial temperature of the object, and k is thecooling rate. Use the definition of a logarithm alongwith properties of logarithms to solve the formula fortime tsuch that tis equal to a single logarithm.The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.A pitcher of water at 40 degrees Fahrenheit is placed into a 70 degree room. One hour later, the temperature has risen to 45 degrees. How long will it take for the temperature to rise to 60 degrees?Using the model in Example 6, estimate the number of cases of flu on day 15.Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.Change the function y=3(0.5)x to one having e as the base.With what kind of exponential model would half-life be associated? What role does half-life play in these models?Is carbon dating? Why does it work? Give an example in which carbon dating would be useful.With what kind of exponential model would doubling time be associated? What role does doubling time play in these models?Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of Cooling would be applied.What is an order of magnitude? Why are orders of magnitude useful? Give an example to explain.The temperature of an object in degrees Fahrenheit after t minutes is represented by the equation T(t)=68e0.0174t+72. To the nearest degree, what is the temperature of the object after one and a half hours?For the following exercises, use the logistic growth model f(x)=1501+8e2x . 7. Find and intercept f(0) . Round to the nearest tenth.For the following exercises, use the logistic growth model f(x)=1501+8e2x . Find and interpret f(4). Round to the nearest tenth.For the following exercises, use the logistic growth model f(x)=1501+8e2x . Find the carrying capacity.For the following exercises, use the logistic growth model f(x)=1501+8e2x . Graph the model.For the following exercises, use the logistic growth model f(x)=1501+8e2x . Determine whether the data from the table could best be represented as a function that is linear, exponential, or logarithmic. Then write a formula for a model that represents the data.For the following exercises, use the logistic growth model f(x)=1501+8e2x . Rewrite f(x)=1.68(0.65)x as an exponential equation with base e to five significant digits.For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t)=10001+9e0.6t . Graph the function.For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t)=10001+9e0.6t . What is the initial population of fish?For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t)=10001+9e0.6t . To the nearest tenth, what is the doubling time for the fish population?For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t)=10001+9e0.6t . To the nearest whole number, what will the fish population be after 2 years?For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t)=10001+9e0.6t . To the nearest tenth, how long will it take for the population to reach 900?For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t)=10001+9e0.6t . What is the carrying capacity for the fish population? Justify your answer using the graph of P .A substance has a half-life of 2.045 minutes. If the initial amount of the substance was 132.8 grams, how many half-lives will have passed before the substance decays to 8.3 grams? What is the total time of decay?The formula for an increasing population is given by p(t)=P0ert where P0 is the initial population and r0. Derive a general formula for the time t it takes for the population to increase by a factor of M .Recall the formula for calculating the magnitude of an earthquake, M=23log(SS0) . Show each step for solving this equation algebraically for the seismic moment S.What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?Prove that bx=exln(b) for positive b1 .For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. To the nearest hour, what is the half-life of the drug?For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. Write an exponential model representing the amount of the drug remaining in the patient’s system after t hours. Then use the formula to find the amount of the drug that would remain in the patient’s system after 3 hours. Round to the nearest milligram.For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. Using the model found in the previous exercise, find f (10) and interpret the result. Round to the nearest hundredth.For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days. Round to the nearest tenth of a gram.For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest minute, what is the half-life of this substance?For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. The half-life of Radium-226 is 1590 years. What is the annual decay rate? Express the decimal result to four significant digits and the percentage to two significant digits.For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. The half-life of Erbium-165 is 10.4 hours. What is the hourly decay rate? Express the decimal result to four significant digits and the percentage to two significant digits.For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. A wooden artifact from an archeological dig contains 60 percent of the carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half-life of carbon-14 is 5730 years.)For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was 1350 bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after 3 hours?For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1,000 bacteria present after 20 minutes. To the nearest whole number, what was the initial population in the culture?For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1,000 bacteria present after 20 minutes. Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double?For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69° F room. After fifteen minutes, the internal temperature of the soup was 95° F. Use Newton’s Law of Cooling to write a formula that models this situation.For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69° F room. After fifteen minutes, the internal temperature of the soup was 95° F. To the nearest minute, how long will it take the soup to cool to 80° F?For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69° F room. After fifteen minutes, the internal temperature of the soup was 95° F. To the nearest degree, what will the temperature be after 2 and a half hours?For the following exercises, use this scenario: A turkey is taken out of the oven with an internal temperature of 165° Fahrenheit and is allowed to cool in a 75° F room. After half an hour, the internal temperature of the turkey is 145° F. Write a formula that models this situation.For the following exercises, use this scenario: A turkey is taken out of the oven with an internal temperature of 165° Fahrenheit and is allowed to cool in a 75° F room. After half an hour, the internal temperature of the turkey is 145° F. To the nearest degree, what will the temperature be after 50 minutes?For the following exercises, use this scenario: A turkey is taken out of the oven with an internal temperature of 165° Fahrenheit and is allowed to cool in a 75° F room. After half an hour, the internal temperature of the turkey is 145° F. To the nearest minute, how long will it take the turkey to cool to 110° F?For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth.For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth.For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth. Plot each set of approximate values of intensity of sounds on a logarithmic scale: Whisper: 1010Wm2 , Vacuum: 104Wm2 , Jet: 102Wm2For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth. Recall the formula for calculating the magnitude of an earthquake, M=23log(SS0). One earthquake has magnitude 3.9 on the MMS scale. If a second earthquake has 750 times as much energy as the first, find the magnitude of the second quake. Round to the nearest hundredth.For the following exercises, use this scenario: The equation N(t)=5001+49e0.7t models the number of people in a town who have heard a rumor after t days. How many people started the rumor?For the following exercises, use this scenario: The equation N(t)=5001+49e0.7t models the number of people in a town who have heard a rumor after t days. To the nearest whole number, how many people will have heard the rumor after 3 days?For the following exercises, use this scenario: The equation N(t)=5001+49e0.7t models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N (t ) approach? Interpret your answer.For the following exercise, choose the correct answer choice. A doctor and injects a patient with 13 milligrams of radioactive dye that decays exponentially. After 12 minutes, there are 4.75 milligrams of dye remaining in the patient’s system. Which is an appropriate model for this situation? a. f(t)=13(0.0805)t b. f(t)=13e0.9195t c. f(t)=13e(0.0839t) d. f(t)=4.751+13e0.83925tTable 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.What is a carrying capacity? What kind of model has a carrying capacity built into its formula? Why does this make sense?What is regression analysis? Describe the process of performing regression analysis on a graphing utility.What might a scatterplot of data points look like if it were best described by a logarithmic model?What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?For the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph. y=10.209e0.294xFor the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph. y=5.5981.912ln(x)For the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph. y=2.104(1.479)xFor the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph. y=4.607+2.733ln(x)For the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph. y=14.0051+2.79e0.812xTo the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t)=1751+6.995e0.68t ? What is the carrying capacity?Rewrite the exponential model A(t)=1550(1.085)x as an equivalent model with base e. Express the exponent to four significant digits.A logarithmic model is given by the equation h(p)=67.6825.792ln(p). To the nearest hundredth, for what value of p does h(p)=62 ?A logistic model is given by the equation S P(t)=901+5e0.42t. To the nearest hundredth, for what value of t does P(t)=45 ?What is the y -intercept on the graph of the logistic model given in the previous exercise?For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x)=681+16e0.28x . Graph the population model to show the population over a span of 3 years.For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x)=681+16e0.28x . What was the initial population of koi?For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x)=681+16e0.28x . How many koi will the pond have after one and a half years?For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x)=681+16e0.28x . How many months will it take before there are 20 koi in the pond?For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x)=681+16e0.28x . Use the intersect feature to approximate the number of months it will take before the population of the pond reaches half its carrying capacity.For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x)=5581+54.8e0.462x , where x is given in years. Graph the population model to show the population over a span of 10 years.For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x)=5581+54.8e0.462x , where x is given in years. What was the initial population of wolves transported to the habitat?For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x)=5581+54.8e0.462x , where x is given in years. How many wolves will the habitat have after 3 years?For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x)=5581+54.8e0.462x , where x is given in years. How many years will it take before there are 100 wolves in the habitat?For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x)=5581+54.8e0.462x , where x is given in years. Use the intersect feature to approximate the number of years it will take before the population of the habitat reaches half its carrying capacity.For the following exercises, refer to Table 7. Use a graphing calculator to create a scatter diagram of the data.For the following exercises, refer to Table 7. Use the regression feature to find an exponential function that best fits the data in the table.For the following exercises, refer to Table 7. Write the exponential function as an exponential equation with base e.For the following exercises, refer to Table 7. Graph the exponential equation on the scatter diagram.For the following exercises, refer to Table 7. Use the intersect feature to find the value of x for which f(x)=4000 .For the following exercises, refer to Table 8. Use a graphing calculator to create a scatter diagram of the data.For the following exercises, refer to Table 8. Use the regression feature to find an exponential function that best fits the data in the table.For the following exercises, refer to Table 8. Write the exponential function as an exponential equation with base e.For the following exercises, refer to Table 8. Graph the exponential equation on the scatter diagram.For the following exercises, refer to Table 8. Use the intersect feature to find the value of x for which f(x)=250 .For the following exercises, refer to Table 9. Use a graphing calculator to create a scatter diagram of the data.For the following exercises, refer to Table 9. Use the LOGarithm option of the REGression feature to find a logarithmic function of the form y=a+bln(x) that best fits the data in the table.For the following exercises, refer to Table 9. Use the logarithmic function to find the value of the function when x=10 .For the following exercises, refer to Table 9. Graph the logarithmic equation on the scatter diagram.For the following exercises, refer to Table 9. Use the intersect feature to find the value of x for which f(x)=7 .For the following exercises, refer to Table 10. Use a graphing calculator to create a scatter diagram of the data.For the following exercises, refer to Table 10. Use the LOGarithm option of the REGression feature to find a logarithmic function of the form y=a+bln(x) that best fits the data in the table.For the following exercises, refer to Table 10. Use the logarithmic function to find the value of the function when x=10 .For the following exercises, refer to Table 10. Graph the logarithmic equation on the scatter diagram.For the following exercises, refer to Table 10. Use the intersect feature to find the value of x for which f(x)=8 .For the following exercises, refer to Table 11. Use a graphing calculator to create a scatter diagram of the data.For the following exercises, refer to Table 11. Use the LOGISTIC regression option to find a logistic growth model of the form y=c1+aebx that best fits the data in the table.For the following exercises, refer to Table 11. Graph the logistic equation on the scatter diagram.For the following exercises, refer to Table 11. To the nearest whole number, what is the predicted carrying capacity of the model?For the following exercises, refer to Table 11. Use the intersect feature to find the value of x for which the model reaches half its carrying capacity.For the following exercises, refer to Table 12. Use a graphing calculator to create a scatter diagram of the data.