Question

A wildfire 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

Exponential growth formula

$f(x)=a(1+r)^x$

where:

• f(x): exponential growth function

,

• a: initial amount

,

• r: growth rate, as a decimal

,

• x: time

In this case, f(x) models the expected population, the initial population is a = 200 deers, the growth rate is r = 0.07 (= 7/100), and x measures time in years. Substituting these values into the formula:

$\begin{gathered} f(x)=200(1+0.07)^x^{} \\ f(x)=200(1.07)^x \end{gathered}$