SOLUTION: -Exponential Growth Problem- The increase of aliens was exponential. After 5 hours the aliens numbered 120, and after 15 hours there were 400 of them. How many aliens were there

Question 1096225: -Exponential Growth Problem-
The increase of aliens was exponential. After 5 hours the aliens numbered 120, and after 15 hours there were 400 of them. How many aliens were there after 25 hours?
-Out of all the exponential growth/decay problems I have solved, this one stumps me. I'd appreciate any help in answering this. Thanks!
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
The equation for exponential growth is P(1)=P(0)e^kt, where P(1) is the resultant population, P(0) is the initial population, k is a constant, and t is time. So:
P(5)=120 and P(15)=400. Therefore:
400/120=e^10k
e^10k=3.33333
ln e^10k=10k ln e=10k ln 3.333333
k=ln 3.33333/10=.1204
So, after 25 hours, you have:
P(25)=400*e^(10)(.1204)
P(25)=1333.37 aliens after 25 hours
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