Chapter 8, Problem 17SGR

(a)

To determine

To find: The function that represents the given situation.

Answer to Problem 17SGR

The model for the population is $A\left(t\right)=120,000{\left(0.97\right)}^t$ .

Explanation of Solution

Given:

The population of the city is $120000$ .

The decrease of population is at the rate of $3\%$ .

Calculation:

Consider the formula for the simple interest is,

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

Then function that represent the situation is,

  $\begin{array}{c}A\left(t\right)=120,000{\left(1-\frac{3}{100}\right)}^t\\ =120,000{\left(0.97\right)}^t\end{array}$

(b)

To determine

To find: The population after ten years.

Answer to Problem 17SGR

The population after 10 years is $88491$ .

Explanation of Solution

Given:

The population is calculated after 10 years.

Calculation:

Consider the model for the population is,

  $A\left(t\right)=120,000{\left(0.97\right)}^t$

Then, the population after 10 years is,

  $\begin{array}{c}A\left(t\right)=120,000{\left(0.97\right)}^{10}\\ =88490.89\\ =88491\end{array}$