SOLUTION: Suppose a population of initial size 100 grows at the rate of 8% per year forever. What is the size of the population at the end of year 1? What is the size of the population at

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Question 163468: Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1?
What is the size of the population at the end of year 2?
What is the size of the population at the end of year 3?
What is the size of the population at the end of year n (for any integer n)?
What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200? Use a calculator to solve to x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
After year 1, the population would be
P%5B1%5D=100%281%2B.08%29=108
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P%5B2%5D=P%5B1%5D%281%2B.08%29=108%281.08%29=116.64=117
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P%5B3%5D=P%5B2%5D%281%2B.08%29=117%281.08%29=126.36=126
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Continuing all the way back to time t=0 years,
P%5Bn%5D=P%5B0%5D%281.08%29%5En
P%5Bn%5D=100%281.08%29%5En
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200=100%281.08%29%5Ex
1.08%5Ex=2
You can use a calculator to iterate for x.
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Algebraically you can solve it using logarithm functions.
x=log%281.08%2C2%29
x=9
Nine years to double the population at 8% growth.