James is contemplating an investment opportunity represented by the function A(t)=P(1.06)t, where P is the initial amount of the investment, and t is the time in years. If James invests $5000, what is the average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20?

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.

Step-by-step explanation:

Given that:

Initial Investment, P  = $5000

Formula:

To find: If James invests $5000,

average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20=?

Solution:

First of all, let us find out A(15) and A(20):

Putting t = 15 first,

Putting t = 20,

Average rate of change / year is defined as:

So, required rate of change:

So, the answer is:

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.