Question

The math SAT score of a high school student graduate can be approximated by S(x)=573-133(0.987), where x is the household income of the student in thousands of dollars per year. What is the average rate of change of the SAT score for students with household incomes ranging from $40,000 to $60,000 per year, in points per thousand dollars? Round answers to 3-decimal places and do not include units with your answer.

Answer 1

Answer: 0.907

Explanation:

The average rate of change in a function from x= a to x = b is given by :-

`(f(b)-f(a))/(b-a)`

Given:
`S(x)=573-133(0.987)^x`

Then, the average rate of change of the SAT score for students with household incomes ranging from $40,000 to $60,000 per year will be :

`(S(60)-S(40))/(60-40)=(573-133(0.987)^(60)-573-133(0.987)^(40))/(20)\\\\=(512.34-494.20)/(20)\\\\=(18.14)/(20)\\\\=0.907`

Hence, the average rate of change of the SAT score for students with household incomes ranging from $40,000 to $60,000 per yearr= 0.907