Chapter 7.6, Problem 19PPE

To determine

To find: the foxes will there after 45 years.

Answer to Problem 19PPE

The population of foxes after 45 years is 4800.

Explanation of Solution

Given information:

A population of 75 foxes in wildlife preserve quadruples in size every 15 yr. The function $y=75\cdot 4^x$ , where $x$ is the number of 15 yr periods, models the population growth.

Calculation:

Consider the function,

  $y=75\cdot 4^x$

Now, solve the function as shown,

  $\begin{array}{c}y=75\cdot 4^x\\ y\left(3\right)=75\left(4^3\right)\\ =75\left(64\right)\\ =4800\end{array}$

So, the population of foxes after 45 years is 4800.