Question

Calculate the average rate of change in the amount of the surcharge for non-account holders between 2004 and 2008. Write the result in a sentence of interpretation. (Round your answer to two decimal places.)

Answer 1

The average rate of change in the amount of the surcharge for non-account holders between 2004 and 2008 is $0.08

Explanation:

Given

`s(t) = 0.72 * 1.081^t`

`3 \le t \le 13`

`t \to` years since 2001

Required

Average rate of change between 2004 and 2008

In 2004,

`t = 2004 - 2001`

`t =3`

So:

`s(t) = 0.72 * 1.081^t`

`s(3) = 0.72 * 1.081^3`

`s(3) = 0.9095`

In 2008,

`t = 2008 - 2001`

`t = 7`

So:

`s(t) = 0.72 * 1.081^t`

`s(7) = 0.72 * 1.081^7`

`s(7) = 1.2420`

The average rate of change (m) is calculated as:

`m = (s(a) - s(b))/(a - b)`

In this case:

`(a,b) = (3,7)`

So, we have:

`m = (s(3) - s(7))/(3 - 7)`

`m = (s(3) - s(7))/(-4)`

Substitute values for s(3) and s(7)

`m = (0.9095 - 1.2420)/(-4)`

`m = (-0.3325)/(-4)`

`m = 0.083125`

`m = 0.08` --- approximated