Answer
a) $284$ hundreds of thousands record highs
b) underestimation by $6$ hundreds of thousands record highs
Work Step by Step
a) As $x=10$ means the tenth decade, $f(10)$ signifies the number of daily high temperatures in the United States in the 2000s (in hundreds of thousands).
We calculate $f(10)$ by substituting $x=10$ in the model's equation:
$$\begin{align*}
f(10)&=10(10^3)-200(10^2)+1230(10)-2016=284.\\
\end{align*}$$
So in the tenth decade the number of record highs was predicted as $284$ hundreds of thousands.
b) We read the value of $f$ from the graph:
$$f(10)=290.$$
Because $284<290$, it means the model underestimates the number of record highs shown by the graph. The value by which the model underestimates the number of record highs from the graph is:
$$290-284=6.$$
