Chapter 3.4, Problem 54E

(a)

To determine

To calculate: The values of average rate of change of S over successive intervals and complete the table contains math SAT score for the critical reading of a high school graduate which can be approximated by $S\left(x\right)=550-136{\left(0.985\right)}^x$ points on the critical reading SAT test, where x is the household income of the student in thousand dollars per year.

Interval	$\left[0,40\right]$	$\left[40,80\right]$	$\left[80,120\right]$	$\left[120,160\right]$	$\left[160,200\right]$
Avg. Rate of Change of S

(b)

To determine

The interpretation of result obtained in part (a) for the interval $\left[40,80\right]$ indicating direction of change and units of measurement if the table contains math SAT score of a high school graduate which can be approximated by $S\left(x\right)=550-136{\left(0.985\right)}^x$ points on the SAT test, where x is the household income of the student in thousand dollars per year.

Interval	$\left[0,40\right]$	$\left[40,80\right]$	$\left[80,120\right]$	$\left[120,160\right]$	$\left[160,200\right]$
Avg. Rate of Change of S	$1.54$	$0.84$	$0.46$	$0.25$	$0.14$

(c)

To determine

The correct option showing direction of SAT score of student, if the household income rises out of the following options.

The options are:

A) Increases.

B) Decreases.

C) Increases, then decreases.

D) Decreases, then increases

(d)

To determine

The correct option showing the effect on the SAT score of student, if the household income increases out of the following options.

The options are:

A) More pronounced.

B) Less pronounced.