Chapter 4, Problem 8STP

To determine

To find: The year in which the population of Clarksville reach 200,000 people.

Answer to Problem 8STP

The year in which the population of Clarksville reach 200,000 people is 1983.

Explanation of Solution

Given:

The given function is $P\left(t\right)=-0.068t^2+7.85t+56$ .

The $t$ is the number of year since 1960.

Calculation:

Consider the given function is,

  $P\left(t\right)=-0.068t^2+7.85t+56$

Consider the value of $t$ for the year 1974 is,

  $\begin{array}{c}t=1974-1960\\ =14\end{array}$

Substitute the value of the time in the above function as,

  $\begin{array}{c}P\left(t\right)=-0.068{\left(14\right)}^2+7.85\left(14\right)+56\\ =152.572\end{array}$

Consider the value of $t$ for the year 1977 is,

  $\begin{array}{c}t=1977-1960\\ =17\end{array}$

Then, the population in the year 1977 is,

  $\begin{array}{c}P\left(t\right)=-0.068{\left(17\right)}^2+7.85\left(17\right)+56\\ =169.798\end{array}$

Consider the value of $t$ for the year 1983 is,

  $\begin{array}{c}t=1983-1960\\ =23\end{array}$

Then, the population in the year 1983 is,

  $\begin{array}{c}P\left(t\right)=-0.068{\left(23\right)}^2+7.85\left(23\right)+56\\ =200.578\end{array}$