   Chapter 10.4, Problem 53E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

SAT Scores by Income The math SAT score of a high school graduate can be approximated by S ( x ) = 573 − 133 ( 0.987 ) x points on the match SAT test,Where x is the household income of the student in thousands of dollars per year.54a. Use technology to complete the following table, which shows the average rate of change of S over successive intervals of length 40. (Round all answers to two decimal places.) [HINT: See Example 4.] Interval [ 0 , 40 ] [ 40 , 80 ] [ 80 , 120 ] [ 120 , 160 ] [ 160 , 200 ] Avg. Rate ofChange of S b. Interpret your answer for the interval [ 40 , 80 ] , being sure to indicate the direction of change and the units of measurement.c. Multiple choice: As her household income rises, a student’s SAT score(A) increases.(B) decreases.(C) increases, then decreases.(D) decreases, then increases.d. Multiple choice: As the household income increases, the effect on a student’s SAT score is(A) more pronounced.(B) less pronounced.

(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 of a high school graduate which can be approximated by S(x)=573133(0.987)x points on the SAT test, where x is the household income of the student in thousand dollars per year.

 Interval [0,40] [40,80] [80,120] [120,160] [160,200] Avg. Rate of Change of S
Explanation

Given Information:

The table contains math SAT score of a high school graduate which can be approximated by S(x)=573133(0.987)x points on the SAT test, where x is the household income of the student in thousand dollars per year.

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

Calculation:

Consider the interval.

Steps to calculate the average rate of change using Excel Spread sheet as follows:

Step1. Name cells A1, B1 and C1 as x, S(x) and Avg. Rate of change respectively.

Step2. Enter the values of x through cells A2 to A7.

Step3. Click on B2 and add the formula “=573133×(0.987)^A2” in the formula tab and drag the formula to the cells through B2 to B7

(b)

To determine

The interpretation of result obtained in part (a) for the interval [40,80] 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(x)=573133(0.987)x points on the SAT test, where x is the household income of the student in thousand dollars per year.

 Interval [0,40] [40,80] [80,120] [120,160] [160,200] Avg. Rate of Change of S 1.35 0.80 0.48 0.28 0.17

(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.

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