Chapter EP, Problem 8.8.4EP

To determine

To find:The population in $2015$.

Answer to Problem 8.8.4EP

The population of black bears in $2015$ is $344$ .

Explanation of Solution

Given information:

The given information is

Amount is $a=400$

Rate is $r=0.75\%$

Time is $t=20$ in $1995$ .

Calculation:

It is given that the population of black bears has been decreasing at the rate of $0.75\%$ per year.

There were $400$ black bears in the state in $1995$ .

Here, the population continues to define at the same rate So 1 = represents the year 1995 and $t=20$ represents the year $2015$ .

An amount decreased by a certain percent over time is given by $y=a{\left(1-r\right)}^t$ .

Here, $a$ is the initial amount, $r$ is the rate of decrease, and $t$ is the time.

As per the data the initial population of black bears is 400 and the population is decreased at the rate of $0.75\%$ per year.

Here, $a$ is the initial amount, $r$ is the rate of decrease, and $t$ is the time.

Here, $a=400,r=0.75\%=0.0075,t=20$ .

Substitute all value into $y=a{\left(1-r\right)}^t$ .

$\begin{array}{c}y=400{\left(1-0.0075\right)}^{55}\\ =400{\left(0.9925\right)}^{55}\\ =400\times 0.86022\\ =344.0888\end{array}$

Therefore, the population of black bears in $2015$ is $344$ .