SOLUTION: A population of 100 grows at a rate of 8% a year forever. What is the size of population at end of year 1? Year 2? Year 3? What is the size of the population at the end of year n (

Question 251618: A population of 100 grows at a rate of 8% a year forever. What is the size of population at end of year 1? Year 2? 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?
I can figure 1-3 years but I am lost on the rest. Could anyone please help? Thank you.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
Po is starting population __ P is present population

P = Po (1 + .08)^n

200 = 100 (1.08)^x

2 = 1.08^x

log(2) = x log(1.08)

log(2) / log(1.08) = x