Chapter 12.3, Problem 78E

(a)

To determine

Is there any point of inflection on the graph of $S^{\prime }$ where the graph compares the total U.S prison population and the average combined SAT score in the United States during the $1970$ s and $1980$ s and this data can be accurately modeled by $S\left(n\right)=904+\frac{1,326}{{\left(n-180\right)}^{1,325}}\left(192\le x\le 563\right)$.

(b)

To determine

What does the concavity of the graph of $S^{\prime }$ telling about prison population and SAT scores where the graph compares the total U.S prison population and the average combined SAT score in the United States during the $1970$ s and $1980$ s and this data can be accurately modeled by $S\left(n\right)=904+\frac{1,326}{{\left(n-180\right)}^{1,325}}\left(192\le x\le 563\right)$.