PART III: MATHEMATICAL MODELING For each of the following, model the described reality with a mathematical formula. Then

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Part Iii Mathematical Modeling For Each Of The Following Model The Described Reality With A Mathematical Formula Then 1 (234.19 KiB) Viewed 48 times

PART III: MATHEMATICAL MODELING For each of the following, model the described reality with a mathematical formula. Then, answer the question asked. a. C. 1. In 2010, the population of Galesburg was 32,195. The Census Bureau expects the population to decline by 0.55% annually. a. Write the population, P, as a function of t, the number of years beyond 2010. b. Calculate the first and second derivatives of P(t). C. When is the population of Galesburg declining fastest? 2. A person's BMI is inversely proportional to the square of a person's height and directly proportional to a person's weight. Write the BMI as a function of height and weight, h and w. b. How much does a person's BMI increase when the weight increases by 10%? Show that the second partials of B(h, w) are equal. 3. Water pressure increases by 14.5 psi for every 33 feet you go down in the ocean. a. Write the pressure, P, as a function of depth, d. b. How much does the pressure increase when the depth is doubled? 4. In Calories, the amount of energy used in jogging is directly proportion to the distance run and to the cube-root of the speed. a. Write the energy use, E, as a function of distance and speed, d and s. b. How much does energy use change if I double the distance while halving the speed? Would I burn more energy by halving the distance and doubling the speed or by doubling the distance and halving the speed? d. Calculate and interpret Ed and Es. C. 5. The period of a freely-swinging pendulum is T = 2n14/9, where T is the period, L is the length a. of the pendulum, and g is the acceleration due to gravity. This is actually one of the ways that g was originally measured. Sir Francis Bacon did so in 1620. If I have a pendulum on Earth that has a period of 2 seconds, what will be its period on the Moon, whose gravity is 1/6th Earth's? b. Calculate and interpret TL and Tg. Show that the second partials are equal. C.