Question

The revenue (in thousands of dollars) from producing x units of an item is modeled by R(x) = 12x -0.005x^2.

Find the average rate of change in revenue as x changes from 1001 to 1008.



The average rate of change in revenue is ____ dollars per unit.
(Do not round until the final answer. Then round to the nearest integer as needed.)

I just need to know how to solve this problem, I know the answer. Thank you!

Answer 1

2

Explanation:

Average rate of change is just the slope.

You want to find the slope of the line that goes through x=1001 and x=1008 while on R(x)=12x-0.005x^2.

So y=R(x)... R(x) will give your corresponding y values for the x's mentioned.

Just plug them in.

R(1001)=12(1001)-0.005(1001)^2=7001.995

R(1008)=12(1008)-0.005(1008)^2=7015.68

So now the question just becomes find the slope of the line that goes through

(1001,7001.995) and (1008,7015.68).

To find the slope of a line given two points: I just lined the points up and subtract vertically. Afterwards I put the second number on top of the first number.

So let's do that!

(1008 , 7015.68)

-(1001, 7001.995)

------------------------------

7 13.685

So the slope also known as the average rate of change here is 13.685/7.

Putting 13.685 divided by 7 into my calculator returns the value 1.955.

This rounded to the nearest integer is 2.

Answer 2

See below.

Explanation:

Average rate of change =( R(1008) - R(1001) ) / (1008 - 1001)

=[ 12(1008) - 0.005(1008)^2 - (12(1001) - 0.005(1001)^2) ] / 7