Chapter 11.5, Problem 97E

SAT Scores by Income The following bar graph shows U.S. math SAT scores as a function of household income.⁵¹

Family income ($1,000)

a. Which of the following best models the data (C is a constant)?

(A) $S\left(x\right)=C-133e^{-0.0131x}$

(B) $S\left(x\right)=C+133e^{-0.0131x}$

(C) $S\left(x\right)=C+133e^{0.0131x}$

(D) $S\left(x\right)=C-133e^{0.0131x}$

( $S\left(x\right)$ is the average math SAT score of students whose household income in x thousand dollars per year.)

b. Use $S\text{'}\left(x\right)$ topredict how a student’s math SAT score is affected by a $\$1,000$ increasein parents’ income for a student whose parents earn $45,000.

c. Does $S\text{'}\left(x\right)$ increasesor decreases as x increases? Interpret your answer.