# Solve for A (Exponents)

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

Equation:

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

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.

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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 $t$.