College Algebra, Chapter 3, 3.4, Section 3.4, Problem 30

The graph gives the number of farms in the United States from 1850 to 2000.

"Please refer to the graph in the book"

a.) Estimate the average rate of change in the number of farms between

i.) 1860 and 1890


$
\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(1890) - f(1860)}{1890 - 1860}
&& \text{Substitute } a = 1860 \text{ and } b = 1890
\\
\\
\text{average rate of change } =& \frac{4500 - 2100}{30}
&& \text{Combine like terms}
\\
\\
\text{average rate of change } =& 80
&& \text{Answer}

\end{aligned}
\end{equation}
$


ii.) and 1950 and 1970


$
\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(1970) - f(1950)}{1970 - 1950}
&& \text{Substitute } a = 1950 \text{ and } b = 1970
\\
\\
\text{average rate of change } =& \frac{2600 - 5500}{20}
&& \text{Simplify}
\\
\\
\text{average rate of change } =& -145
&& \text{Answer}

\end{aligned}
\end{equation}
$


b.) In which decade did the number of farms experience the greatest average rate of deadline?

Based from the graph, the greatest average rate of deadline occurs during 1950 to 1960.