Question

The amount of money in an investment is modeled by the function A(t)=750(1.0258)^t. The variable A represents the investment balance in dollars, and t the number of years.

What is the doubling time for the investment?

Answer 1

We started with $750.00 so we want to know when A = 1.500.00
1,500 = 750 * (1.0258)^t
1,500 / 750 = 1.0258^t
Taking logs of both sides:
log (2) = t * log(1.0258)
t = log (2) / log(1.0258)
t = .301029996 / 0.0110626947
t = 27.2112720289 years

And to check that answer, try this page:
http://www.1728.org/compint.htm