Question

A wildlife biologist determines that there are approximately 200 deer in a region of a national park. The population grows at a rate of 7% per year. What is an exponential function that models the expected population?

Answer 1

The exponential function is Y = 200 [1.07]ˣ

Explanation:

Let Y represent the expected population

Let P represent the current population

Let r represent the population growth rate

let x represent the number of years or nth year.

The compound interest expression can used to derive the exponential function can be represented as follows

Y = P [1 + (r ÷ 100)]ˣ

Y = 200 [ 1 + (7 ÷ 100)]ˣ

Y = 200 [ 1 + (0.07)]ˣ

Y = 200 [1.07]ˣ