College Algebra, Chapter 3, 3.4, Section 3.4, Problem 24

The graph represents the population $P$ in a small industrial city from 1950 to 2000. The variable $x$ represents the number of years since 1950.

"Please refer to the graph in the book"

a.) What was the average rate of change of $P$ between $x = 20$ and $x = 40$?


$\begin{equation} \begin{aligned} \text{average rate of change } =& \frac{f(b) - f(a)}{b - a} && \text{Model} \\ \\ \text{average rate of change } =& \frac{f(40) - f(20)}{40 - 20} && \text{Substitute } a = 20 \text{ and } b = 40 \\ \\ \text{average rate of change } =& \frac{40 - 40}{20} && \text{Simplify} \\ \\ \text{average rate of change } =& \frac{0}{20} && \text{Simplify} \\ \\ \text{average rate of change } =& 0 && \text{Answer} \end{aligned} \end{equation}$


b.) Interpret the value of the average rate of change that you found in part (a).

There is no average rate of change of the population between 1970 to 1990.