SOLUTION: After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The rat population on the island grows exponentially, and after 15 months there 280 rats on the

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Question 830622: After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The rat population on the island grows exponentially, and after 15 months there 280 rats on the island.
a) Find the function that models the population "t" months after the arrival of the rats
b) What will the population be in 3 years after the shipwreck.
c) When will the population reach 2000
Reviewing for a test. I had trouble with this early, and still struggling with these word problems. Please help.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Model generally as p=Ie%5E%28kt%29, t is in months, I is initial population, k is a constant needing to be found.

Solve symbolically now, for k.
ln%28p%29=ln%28I%29%2Bln%28e%5E%28kt%29%29
ln%28p%29=ln%28I%29%2Bkt%2A1
kt=ln%28p%29-ln%28I%29
kt=ln%28p%2FI%29
highlight_green%28k=%281%2Ft%29ln%28p%2FI%29%29
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Compute value of k.
k=%281%2F15%29ln%28280%2F120%29
highlight_green%28k=0.0565%29
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Specific model for this example rat population:
highlight%28p=120%2Ae%5E%280.0565%2At%29%29

REMINDER: t is in MONTHS