Answer
A) The model predicts that $ 3.9\%$ of Americans earning $\$ 60$ thousand report fair or poor health. The result underestimate the percentage displayed in on the graph by $0.1\%$.
B) About $\$10$ thousand annual income correspond to $24\%$ reporting fair or poor health.
Work Step by Step
Given
$$ f(x)=-4.4 \sqrt{x}+38$$
Part A
\begin{equation}
\begin{aligned}
f(60)&=-4.4 \sqrt{60}+38\\
& = 3.9\% \\
\end{aligned}
\end{equation}
The model predicts that $ 3.9\%$ of Americans earning $\$ 60$ thousand report fair or poor health. The result underestimate the percentage displayed in on the graph by $0.1\%$.
Part B Set $f(x)= 24$ and solve for $x$.
\begin{equation}
\begin{aligned}
f(x)&=24\\
-4.4 \sqrt{x}+38& = 24 \\
-4.4 \sqrt{x}& = 24-38\\
-4.4 \sqrt{x}& = -14\\
\left(\sqrt{x}\right)^2&= \left(\frac{14}{4.4}\right)^2\\
x&= 10.12\approx 10\\
\end{aligned}
\end{equation}
About $\$10$ thousand annual income correspond to $24\%$ reporting fair or poor health.
