Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Question: The area covered by a newly-introduced species of invasive weed doubles every 4 years. Suppose the weed currently covers 23 km^2.

a) Write an equation that gives the area, A, covered by the weed, in t years. b) Estimate how many years it will take for the weed to cover 51 km^2


$$A = 23(2)^{t/4}$$

I could keep plugging in values till I get the correct but how would I reverse the equation to get t when A = 51?

I really need to understand this stuff for a test tomorrow... I jumped into a course 3 weeks late and this is what I get hit with.

share|cite|improve this question
HINT: $ \log_b{x^y} \equiv y\log_b{x} $ – Orbling Mar 4 '11 at 0:36

Logarithms are your friend. You have $A = 23(2)^{t/4}$, which means that $$\ln(A) = \ln(23(2)^{t/4}) = \ln(23) + \ln(2^{t/4}) = \ln(23) + \frac{t}{4}\ln(2).$$ If you know $A$, you can use this to figure out $t$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.