Chapter 4.5, Problem 98E

SAT Scores by Income The following bar graph shows U.S. critical reading SAT scores as a function of household income.⁵²

Family income ($1,000)

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

(A) $S\left(x\right)=C+\frac{1}{136e^{0.015x}}$

(B) $S\left(x\right)=C-136e^{0.015x}$

(C) $S\left(x\right)=C-\frac{136}{e^{0.015x}}$

(D) $S\left(x\right)=C-\frac{e^{0.015x}}{136}$

( $S\left(x\right)$ 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.