Future Population

Question

The initial population of a town is 4500 and it grows with a doubling time of 10 years. What will the population be in 8 years?

Answer 1

There are a few ways to approach this population growth problem. They are all exponential growth problems; here are a couple of approaches:

1) Use the basic exponential growth equation: y = ab^x where y is the future population, a is your initial population, b is your base, and x is time in years.

(a) So, y = 4500b^x and since the population doubles in 10 years we can write 9000 = 4500b¹⁰. Solving for b we get b = 2^1/10.

(b) We then can rewrite equation to be y=4500(2^1/10)^x=4500(2)^x/10. If x=8, we can solve y=4500(2)^8/10≈7835.

2) Use the continuous growth equation with base e, y=ae^rx, where r is the exponential growth rate.

(a) As before, y=4500e^rx and letting the population double we get 2=e^10r. Solving for r by taking the natural logarithm we get r≈0.693.

(b) We then can write the equation y=4500e^0.693x. If x=8, we can solve y=4500e^0.693(8)≈7835.