Chapter 11.5, Problem 98E

(a)

To determine

The correct option that models the data in the graph showing critical reading SAT scores as a function of household income where C is a constant out of the following options.

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

Where $S\left(x\right)$ is the average critical reading SAT score of students with household income x in thousand dollars per year.

(b)

To determine

The prediction for the effect on the critical reading SAT score of the student if the income of parents earning $\$45000$ is increased by a $\$1000$ using $S^{\prime }\left(x\right)$ Where $S\left(x\right)$ is the average critical reading SAT score of students with household income x in thousand dollars per year. The graph showing critical reading SAT scores as a function of household income where C is a constant.

(c)

To determine

Whether $S^{\prime }\left(x\right)$ is increasing or decreasing as x increases and also interpret the result if $S\left(x\right)$ is the average math SAT score of students with household income x in thousand dollars per year and the graph showing critical reading SAT scores as a function of household income where C is a constant.