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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

Question 176776: 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.
Found 2 solutions by Mathtut, stanbon:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
formula is P = 100(1+int rate %)^t
:
so in our case P=100%281.08%29%5Et
:
I will do year 2 P=100%281.08%29%5E2=100%281.1664%29=116.64

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
100*(1.08)
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What is the size of the population at the end of year 2?
100(1.08)^2
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What is the size of the population at the end of year 3?
100(1.08)^3
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What is the size of the population at the end of year n (for any integer n)?
100(1.08)^n
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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.
100(1.08)^n = 200
1.08^n = 2
n = log(2)/log(1.08) = 9.0064 years
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Cheers,
Stan H.