Suppose that in a memory experiment the rate of memorizing is given by M'(t) = – 0.006t +0.8t where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 20 min (from t= 0 to t= 20)? In the first 20 minutes words are memorized.

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

A:

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

A:

Q: What is the amount of salt in the tank at time t = 0?

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: A culture of yeast grows at a rate proportional to its size. If the initial population is 4000 cells…

A: Let's find.

Q: 2. A 13-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the…

A:

Q: Suppose that a shallow earthquake occurs in which the P waves travel 8 km/sec and the S waves travel…

A:

Q: ologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Answer

Q: if two resistors with resistances R1 and R2 are connected parallel, then the total Resistance R…

A: Given,

Q: Suppose the quantity (in grams) of a radioactive substance present at time t isQ(t) =…

A: Radioactive substances have different rates of decomposition.

Q: 25. A 10-foot ladder is placed against a vertical wall. Suppose that the bottom of the ladder slides…

A: Given :-  dx/dt= 3feet/sec  Ladder height= 10feet  Find rate at which ladder is sliding down from…

Q: A bacteria population starts with 400 bacteria and grows ata rate of  r(t) = (450.268)…

A:

Q: A rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the  rate of change of length.

Q: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2…

A:

Q: The rate at which radioactive nuclei decay is proportional to the number of nuclei that are present…

A:

Q: 3. A 20 ft ladder is leaning against a wall and begins to slide. How fast is the top of the ladder…

A: A 20ft ladder is leaning against a wall and begins slide.The ladder is 12ft away from the wall and…

Q: A bacteria population starts with 400 bacteria and grows at a rate of r(t)= 450.268 e ^1.12567t per…

A:

Q: A 15-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of…

A:

Q: the number of U.S. Citizens aged 65 year and older from 1900 through 2050 is estimated to be growing…

A: Given: Rt=0.063t2-0.48t+3.87 As it is given that 0≥t≤15 Hence, t=0 for 1900 and t=10 for 2000 and…

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

Q: 2. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at…

A:

Q: If two resistors with resistance R1 and R2 are connected in parallel, the total resistance R in ohms…

A:

Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: The rate at which the height of the tree changes is given by,h'(t)=3t2+t    ft/yr…

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: If the instantaneous growth rate of COVID19 is modeled by (limHh->0)(200t+100h). At t=5 seconds…

A:

Q: A tank contains 4000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure…

A: Here, ri = 4, ci = 0, r0 = 5, The differential equation is There is no inflow of salt, thus the…

Q: A forester finds that a certain type of forest tree grows in such a way that its height h(t) after t…

A:

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: A tank contains 1000 liters (L) of a solution consisting of 170 kg of salt dissolved in water. Pure…

A: The rate of change of a quantity with respect to time is the differential of that quantity. In a…

Q: If 150 g of copper at initial temperature of 50 °C gains 6930 J of heat when it is cooled to 170°C.…

A:

Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this…

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

Q: A tank contains 5000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: 10) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: 20. A 13 foot ladder leans against a vertical wall. When the ladder is pulled away from the wall at…

A:

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

A:

Q: A tank contains 1000 liters (L) of a solution consisting of 100 kg of salt dissolved in water. Pure…

A: Consider, is the Rate of pure water is pumped into the tank is equal to 5 L/s. Formula used,

Q: Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has…

A: Exponential growth/decay is given by dxdy=rici-r0vx here, ri=3= rate of drug entering. and r0=3=…

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A:

Q: A certain radioactive substance has a half-life of 50 hours. Find how long it will take for 90% of…

A:

Q: 4. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard's average…

A: Given: a) A lizard accelerates from 2 m/s to 10m/s in 4 seconds. What is lizards average…

Q: A 50L tank initially contains 5L of brine solution where 3kg of salt have been dissolved. At t = 0,…

A: According to the given information,

Q: How do you solve question 2?

A: Let x= horizontal distance y= vertical distance Given that dx/dt=1 ft/sec We have to find dy/dt at…

Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.