word problem

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word problem

The number of rabbits increased exponentially. At first there were 400. Three years later there were 1600. Approximately how many rabbits would there be at the end of 10 years?
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Re: word problem

1600 = 400 e^(k)(3)
e^3k = 4
ln(e^3k) = ln 4
3k = ln 4

ln 4
----- = k
 3

k = 0.4621


r = 400e^(0.4621)(x)
r = 400e^(0.4621)(10)   ← solving for 10 years
r = 400e^4.621
r = 400(101.6)
r = 40,640 rabbits after 10 years

- Proof