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 n (for any integer n)? What algebraic equa

Algebra ->  Polynomials-and-rational-expressions -> 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 n (for any integer n)? What algebraic equa      Log On


   

Question 133078: 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 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?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the population in any year would be
f%28x%29+=+100+%281.08%29%5En+
So to solve for a population of 200
f%28x%29+=+100+%281.08%29%5En+
200+=+100+%281.08%29%5En+
2+=+%281.08%29%5En+
Plug in a few numbers and you'll find that about 9 years will double the population (that is a handy thing to know when calculating interest too. Remember the 'rule of 72'. Divide 72 by the interest rate (in this case 8) and see that is will take about 9 years to double.