Answer:
The average rate of change in the amount of the surcharge for non-account holders between 2004 and 2008 is $0.08
Step-by-step explanation:
Given
[tex]s(t) = 0.72 * 1.081^t[/tex]
[tex]3 \le t \le 13[/tex]
[tex]t \to[/tex] years since 2001
Required
Average rate of change between 2004 and 2008
In 2004,
[tex]t = 2004 - 2001[/tex]
[tex]t =3[/tex]
So:
[tex]s(t) = 0.72 * 1.081^t[/tex]
[tex]s(3) = 0.72 * 1.081^3[/tex]
[tex]s(3) = 0.9095[/tex]
In 2008,
[tex]t = 2008 - 2001[/tex]
[tex]t = 7[/tex]
So:
[tex]s(t) = 0.72 * 1.081^t[/tex]
[tex]s(7) = 0.72 * 1.081^7[/tex]
[tex]s(7) = 1.2420[/tex]
The average rate of change (m) is calculated as:
[tex]m = \frac{s(a) - s(b)}{a - b}[/tex]
In this case:
[tex](a,b) = (3,7)[/tex]
So, we have:
[tex]m = \frac{s(3) - s(7)}{3 - 7}[/tex]
[tex]m = \frac{s(3) - s(7)}{-4}[/tex]
Substitute values for s(3) and s(7)
[tex]m = \frac{0.9095 - 1.2420}{-4}[/tex]
[tex]m = \frac{-0.3325}{-4}[/tex]
[tex]m = 0.083125[/tex]
[tex]m = 0.08[/tex] --- approximated
