Answer:
9.9 years
Explanation:
There are two ways to go at this. For this problem, they give the same answer.
Quick way:
The interest rate is 7.25%. Using the "rule of 72" the doubling time in years is ...
doubling time in years = 72/(interest rate %)
72/7.25 ≈ 9.9 . . . years
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Exact Calculation:
The initial investment is 750, so it will be double when A(t) = 1500. Filling in the value and solving for t, you have ...
1500 = 750(1.0725^t)
2 = 1.0725^t . . . . . . divide by 750
log(2) = t·log(1.0725) . . . . . take logarithms
Divide by the coefficient of t
t = log(2)/log(1.0725) ≈ 9.9 . . . . years