The projected value of an investment is modeled by the exponential function V(t)=30,000(1.125)t , where V(t) is the total value after t years.

Question

What is the percent increase each year for the investment?

Answer 1

For exponential growth, the percent increase is constant from year to year, so you can compute this by using any one year period. It's easiest to do:

V(0) = 30000*(1.125)^0 = 30000

V(1) = 30000*(1.125)^1 = 33750

...giving an (absolute) increase of 3750. The relative increase is 3750 / 30000 = 0.125 = 12.5%.

Note that you can also read off the value of 0.125 directly from the formula; that's a quicker solution but doesn't help to explain why the answer is correct.