Chapter 4.5, Problem 97E

(a)

To determine

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

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

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

(b)

To determine

The prediction for the effect on the math 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 math SAT score of students with household income x in thousand dollars per year.

(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 shows math SAT scores as a function of household income where C is a constant.