Chapter 7.7, Problem 35PFA

To determine

To find the population in the town after 8 years.

Answer to Problem 35PFA

The population in 8 years will be 12,503 & option A is correct.

Explanation of Solution

Given:

A small town currently has a population of 15,000 and each year population decreases by 2.25%

Calculation:

Given,

  $a=15,000,r=2.25\%=0.0225,t=8$

Let p (t) be the population of the town at any time t. Then

  $P\left(t\right)=a{\left(1-r\right)}^t$

Now the population after 8 years is,

  $\begin{array}{l}P\left(t\right)=a{\left(1-r\right)}^t\\ \Rightarrow P\left(8\right)=15000{\left(1-0.0225\right)}^8\\ \Rightarrow P\left(8\right)=15000{\left(0.9775\right)}^8\\ \Rightarrow P\left(8\right)=15000\left(0.833554\right)\\ \Rightarrow P\left(8\right)=12503.32\\ \Rightarrow P\left(8\right)\approx 12503\end{array}$

Therefore the population in 8 years will be 12,503.

Hence option A is correct.