# Population decline.

I'm looking at a question here and I'm a bit confused on how I'm supposed to solve it.

A population of 460 decreases at 5% monthly. How many years will it take for there to be 100 left on the island?

I know I'm supposed to use the formula A = Pe^(rt) where A = 100, P = 460, r = 0.05 * 12, and t is the unknown value. But since the population is decreasing, is the rate supposed to be negative too?

Assuming that the rate is supposed to be negative, I think the next step is supposed to be:

ln(100) = .6x * ln(460) ln(100) / ln(460) = .6x

x = [ln(100) / ln(460)] / .6

But I think this is the wrong answer anyway because that would mean t is approximately 1 year. And this answer wouldn't change even if I used a negative rate. I'm not sure what I'm doing wrong here.

Your equation is correct. $100 = 460*e^{-.6t}$. So $ln(\frac {100}{460})=-.6t$ and $t=2.5434$ years.

• Thank you. I do have one question though. Is population always continuously compounded? How do I know that I'm not supposed to use A = P(1+r/n)^nt? – Alphatron Mar 11 '16 at 4:46