Question

The revenue​ (in dollars) from the sale of x car seats for infants is given by the following function. R(x) =56x -0.020x^2 0less than or equal to x and 2800 is greater than or equal to x

Answer 1

`Rate = 15`

Explanation:

Given

`R(x) = 56 - 0.020x^2`

Required

Find the average change from​ 1,000 car seats to​ 1,050 car seats --- Missing information

This is calculated using:

`Rate = (R(b) - R(a))/(b-a)`

In this case:

`a = 1000`

`b = 1050`

Now, we have:

`Rate = (R(1050) - R(1000))/(1050-1000)`

`Rate = (R(1050) - R(1000))/(50)`

Calculating R(1050)

`R(1050) = 56 *1050- 0.020*1050^2`

`R(1050) = 58800-22050`

`R(1050) = 36750`

Calculating R(1000)

`R(1000) = 56 *1000- 0.020*1000^2`

`R(1000) = 56000- 20000`

`R(1000) = 36000`

So:

`Rate = (R(1050) - R(1000))/(50)`

`Rate = \frac{750} {50}`

`Rate = 15`

The average rate of change is 12