Chapter 9.6, Problem 40PPS

To determine

The deer population be in 2015

Answer to Problem 40PPS

The deer population be in 2015 is $819200$

Explanation of Solution

Given information:

The deer population at a national park doubles every year. In 2000, there were 25 deer in the park and the function is $N=25{\left(2\right)}^t$ The number of deer N in the park t years after 2000

So the value of t is $\begin{array}{c}t=2015-2000\\ t=15\end{array}$

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
  $\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To solve the given equation, for the deer population be in 2015 is as below:

  $\begin{array}{l}N=25{\left(2\right)}^t\\ =25{\left(2\right)}^{15}\\ =25\times 32768\\ =819200\end{array}$

Thus , the deer population be in 2015 is $819200$