16. A wild animal preserve can support no more than 200 elephants. 30 elephants were known to be in the preserve in 1980. Assume that the rate of growth of the population is proportional to how close the population is to this maximum, with a growth constant of 0.01 and time measured in years. (a) Set up a differential equation and solve it to show why the number of elephants can be modeled by the function y(t) = 200 - 170e-0.014 (b) Using the answer in (a), how long will it take for the elephant population to double from the number in 1980? Round your answer to 2 decimal places.

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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.