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

Algebra ->  Exponents -> SOLUTION: Suppose a population of intial size 100 grows at the rate of 8% per year forever. What is the size of the population at the end of year 1? that is the size of the population at the      Log On


   

Question 183543: Suppose a population of intial size 100 grows at the rate of 8% per year forever. What is the size of the population at the end of year 1? that 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 2007? Use a calculator to solve for x.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.