Kaushal B. answered • 3d

Experienced Math and SAT/ACT Tutor

Yes, you are correct that you would divide by 130 first. However, since P is population in thousands, on the left side of the equation you should have **170**, not 17,000. This leaves us with approximately:

1.31 = (1.03)^{x}

Now, if we take the log base 1.03 of both sides, we will just have x on the right side (becase log_{n}(n^{x}) = x), and the answer on the left:

log_{1.03}(1.31) = x

If you can just calculate this logarithm on a calculator for this class, you can plug this in and get your answer of approximately **9 years**.

If your calculator doesn't allow a custom base for your log and you can only use ln, you will have to use the change of base formula:

log_{1.03}(1.31) = **ln(1.31) / ln(1.03)**, and then solve that on your calculator, giving you the same answer of **9 years**.