<PRE><B>Question 183543</B>
Suppose a population of intial size 100 grows at the rate of 8% per year forever
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What is the size of the population at the end of year 1? 
A(1) = 100(1.08) = 108
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What is the size of the population at the end of year 2? 
A(2) = 100(1.08)^2 = 116.64
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What is the size of the population at the end of year 3? 
A(3) = 100(1.08)^3 = 125.97
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What is the size of the population at the end of year n (for any integer n)?
A(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 2007? Use a calculator to solve for x.
A(x) = 100(1.08)^x
1.08^x = [A(x)/100]
x ={log[A(x)/100] / [log(1.08)]}
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Cheers,
Stan H.
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