SOLUTION: Can you help me with this word problem? Thanks! A population of rabbits is growing exponentially at a rate of 11.2% every 2 months. How many months will be required for the rabb

Question 312446: Can you help me with this word problem? Thanks!
A population of rabbits is growing exponentially at a rate of 11.2% every 2 months. How many months will be required for the rabbit population to double?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A population of rabbits is growing exponentially at a rate of 11.2% every 2 months. How many months will be required for the rabbit population to double?
.
Exponential growth/decay formula:
N(t) = No*e(r*t)
.
N(t) = Future Population
No = Starting population
r = growth rate
t= number of months
.
From:"rabbits is growing exponentially at a rate of 11.2% every 2 months" we can determine r (growth rate):
Let x = initial population
.
N(t) = No*e(r*t)
1.112(x) = x*e(r*(2))
1.112 = e(r*(2))
ln(1.112) = r*(2)
ln(1.112) = 2r
ln(1.112)/2 = r
.
Now, we can answer: "How many months will be required for the rabbit population to double?"
N(t) = No*e(r*t)
N(t) = No*e((ln(1.112)/2)*t)
2x = x*e((ln(1.112)/2)*t)
2 = e((ln(1.112)/2)*t)
ln(2) = (ln(1.112)/2)*t
ln(2)/(ln(1.112)/2) = t
13.06 = t
Or,
13 months = t

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