SOLUTION: The doubling time of a population of grasshoppers is 15 days. By what factor does the population of grasshoppers grow in 55 days? (Round to the nearest tenth.)

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Question 941757: The doubling time of a population of grasshoppers is 15 days. By what factor does the population of grasshoppers grow in 55 days?
(Round to the nearest tenth.)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Exponential growth in general, y=Ie%5E%28kt%29;
y, population after time t
t, time in days
I, initial population, assumed t=0
k, growth constant

ln%28y%29=ln%28I%29%2Bkt
kt=ln%28y%29-ln%28I%29
k=%281%2Ft%29%28ln%28y%2FI%29%29
Use the formula to determine value for k.
k=%281%2F15%29%28ln%282%29%29


You may be able to use 15 and 55 to find the factor, knowing that 15 days is the DOUBLING time.
... but continuing with the growth model,
k=0.0462
y=Ie%5E%280.0462t%29, the specific model
Let t=55.
y=1%2Ae%5E%280.0462%2A55%29
highlight%28y=12.7%29