Answer
A) The model predicts that $ 16\%$ of Americans earning $\$ 25$ thousand report fair or poor health. The result overestimates the percentage displayed in on the graph by $1\%$.
B) About $\$30$ thousand annual income correspond to $14\%$ reporting fair or poor health.
Work Step by Step
Given
$$ f(x)=-4.4 \sqrt{x}+38$$
Part A
\begin{equation}
\begin{aligned}
f(25)&=-4.4 \sqrt{25}+38\\
& = 16\% \\
\end{aligned}
\end{equation}
The model predicts that $ 16\%$ of Americans earning $\$ 25$ thousand report fair or poor health. The result overestimate the percentage displayed in on the graph by $1\%$.
Part B Set $f(x)= 14$ and solve for $x$.
\begin{equation}
\begin{aligned}
f(x)&=14\\
-4.4 \sqrt{x}+38& = 14 \\
-4.4 \sqrt{x}& = 14-38\\
-4.4 \sqrt{x}& = -24\\
\left(\sqrt{x}\right)^2&= \left(\frac{24}{4.4}\right)^2\\
x&= 29.75\approx 30\\
\end{aligned}
\end{equation}
About $\$30$ thousand annual income correspond to $14\%$ reporting fair or poor health.
