Answer
The percentage of students who anticipated a starting salary of $\$40$ thousand is $19.7$% .
Work Step by Step
The calculated value using the provided function $p=-0.01{{s}^{2}}+0.8s+3.7$ is greater than the value obtained from the graph in Exercise $13$ .
Consider that the percentage of college students, $p$, who anticipated a starting salary $s$, in thousands of dollars is modeled by:
$p=-0.01{{s}^{2}}+0.8s+3.7$
Put $s=40$ in the provided formula and solve for $p$.
Thus,
The percentage of students who anticipated a starting salary of $\$40$ thousand is given as,
$\begin{align}
& p=-0.01{{\left( 40 \right)}^{2}}+0.8\left( 40 \right)+3.7 \\
& =-0.01\left( 1600 \right)+32+3.7 \\
& =-16+32+3.7 \\
& =19.7
\end{align}$
Therefore, the percentage of students who anticipated a starting salary of $\$40$ thousand is $19.7$% .
Refer to the solution of exercise 13 for the percentage of students who anticipated a starting salary of $\$40$ thousand using the provided graph, which is determined to be $14$% .
Compare it with the obtained solution:
Hence, the calculated value using the provided function is greater than the value obtained from the graph in Exercise $13$.
