! Required information The growth of populations of organisms has many engineering and scientific applications. One of the simplest models assumes that the rate of change of the population p is proportional to the existing population at any time t dt = kgP where kg = the growth rate. Given, the step size = 5 years. The world population, in millions, from 1950 to 2000 is given below: t (yr) 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 P 2555 2780 3040 3346 3708 4087 4454 4850 5276 5686 6079 Assuming the given equation holds, use the data from 1950 through 1970 to estimate kg. (Round the final answer to four decimal places.) The estimate of the population growth rate is kg- = /yr.
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- Q8): To find how much heat is required to bring a kettle of water to its boiling point, you are asked to calculate the specific heat of water at 61°C. The specific heat of water is given as a function of time in Table below. Temperature, T Specific heat, C₂ (°C) J kg-°C 22 42 52 82 100 4181 4179 4186 4199 4217 Determine the value of the specific heat at 7=61°C using the direct T method of interpolation and a third order polynomial. Find the absolute relative approximate error for the third order polynomial approximation (Lagrange Method).is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². DO C.D Frontly у Your tasks: No Deflection m k Fg = mg Initial Condition y m k Write down an expression for the total energy If as the sum Write down an expression for the total energy H Fg = mg Figure 3: System schematic for Problem 4. Yi & X Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. as the sum of potential and kinetic energy in terms of y, y, yi C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of…The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P, has doubled in 7 years, how long will it take to triple? (Round your answer to one decimal place.) yr How long will it take to quadruple? (Round your answer to one decimal place.) yr еВook
- is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². No Deflection m k Fg = mg Initial Condition m k Fg = mg Figure 3: System schematic for Problem 4. Yi 8 Your tasks: A Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. B Write down an expression for the total energy H as the sum of potential and kinetic energy in terms of y, y, yi and element parameters. Will H change as the mass moves? C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of position, y, the initial…b) The variation in the experimental density of water, p, with temperature T, in the range of 20°CA flat plate, maintained at 250 C is placed vertically in air at a pressure of 1 bar and temperature of 20 C. The plate height and width are 20 cm and 10 cm. Find the rate of heat transfer to this plate. [Ans.: 64 W].HW4 EX1: An automobile moving over a rough road (Fig. 1.64) can be modeled considering (a) weight of the car body, passengers, seats, front wheels, and rear wheels; (b) elasticity of tires (suspension), main springs, and seats; and (c) damping of the seats, shock absorbers, and tires. Develop three mathematical models of the system using a gradual refinement in the modeling process. FIGURE 1.64 An automobile moving on a rough road. EX2 1.5* The consequences of a head-on collision of two automobiles can be studied by considering the impact of the automobile on a barrier, as shown in Fig. 1.65. Construct a mathematical model by considering the masses of the automobile body, engine, transmission, and suspen- sion and the elasticity of the bumpers, radiator, sheet metal body, driveline, and engine mounts. FIGURE 1.65 An automobile colliding with a barrier.Designing safe boilers depends on knowing how steam behaves under certain changes in temperature and pressure. Steam tables, such as the one below, are published giving values of the function V = f(T, P) where V is the volume (in cubic feet) of one pound of steam at a temperature of T (in degrees Fahrenheit) and pressure P (in pounds per square inch). T//P 480 500 520 540 20 22 24 26 27.85 25.31 23.19 21.39 28.46 25.86 23.69 21.86 29.06 26.41 24.20 22.33 29.66 26.95 24.70 22.79 a) Find the tangent plane to V = f(T, P) for T near 520°F and P near 24 lb/in². [Hint: Use the tables to approximate your partial derivatives and recall the equation of our tangent plane is: V = VT(T − To) + Vp(P - Po) + f(T, P) ] b) Use the tangent plane to estimate the volume of a pound of steam at a temperature of 525°F and P near 24.3 lb/in².In medical literatures, local blood perfusion rate is typically presented as xx ml/(min 100g tissue), in another word, it represents xx ml of blood supplied to a tissue mass of 100 g per minute to satisfy its nutritional needs. As we learned from the course lectures, the local blood perfusion rate appearing in the Pennes bioheat equation is in a unit of 1/s, or can be interpreted as xx ml of blood supplied to a tissue volume of 1 ml per second. The following lists the blood perfusion rates in various organs or structures in a human body from medical textbooks: brain (50 ml/(min 100g tissue)), kidney (35 ml/(min 100g tissue)), and muscle at rest (3 ml/(min 100g tissue)). Please convert the above local blood perfusion rates into values with the unit of 1/s, therefore, they can be used in the Pennes bioheat equation. The tissue density in a human body is 1050 kg/m³.Q(2) Complete the blank cells in the following table of properties of steam. In the last column describe the condition of steam as compressed liquid, saturated mixture, superheated vapor, or insufficient information; and, if applicable, give the quality. Р (кра) T ('C) v, m'/kg u, KJ/Kg Phase description 300 35 130.24 313.22 135 600 1.34139 275 0.500 600 3090Consider a process to prepare a metal for a certain application. There are five parameters that must be considered: temperature, quenching rate, cooling time, carbon content, CO₂ concentration. It is desired to determine which of these parameters has the most influence on the process. There are two levels for each parameter as shown below. Temperature (°C) Quenching Rate(°C/s) Cooling time (s) Carbon Content (wt% C) CO₂ Concentration (%) Eight experiments were defined as follows: Experiment Carbon Content (wt% C) 1 2 3 4 5 6 7 8 1) What size orthogonal array should be used for evaluation (assume noise is negligible)? 2) Generate the array with the level values (i.e. Level 1 and Level 2). 1 1 1 1 6 6 6 6 Quenching Rate (°C/s) 35 35 140 140 35 35 140 140 Four trials were run for the experiments defined above: Experiment 1 2 3 4 5 6 7 8 Level 1 760 35 1 1 5 T1 68.00 69.84 74.36 71.71 91.27 54.39 64.65 60.31 Cooling Time 1 1 300 300 300 300 1 1 T2 61.41 64.76 61.30 58.42 90.89 Level 2 900…A grocery store sells 5-lb bags of mangoes. You purchase four bags over the course of a month and weigh the mangoes each time. You obtain the following measurement: Week 1 weight: 4.8 lb Week 2 weigh: 5.3 lb Week 3 weigh: 4.9 lb Week 4 weigh: 5.4 lb Does the measurement have random error? Does the measurement have systematic error?SEE MORE QUESTIONS