Math College Algebra

Question

The population of a southern city follows the exponential law. If the population doubled in size over 26 months and the current population is 20,000, what will the population be 4 years from now?

Answer 1

Hello, thank you for taking the time to post your question!

Exponential growth means that we’re modeling this scenario using the formula

P(t) = P0 * e^(rt)

What we’re trying to find is P(48), meaning the population after 4 x 12 = 48 months

P(48) = 20000 * e^(48r)

“r” is the growth rate, which we can find based on the double time … if it says that it doubles every 26 months that means that

r = ln(2) / 26

so the full equation is

P(48) = 20000*e^(48 * ln(2)/26)

When I plug that into my calculator I get 71,908, meaning that the population of the town after 4 years if it keeps growing at this rate will be 71,908.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

A = Pe^rt

2=e^24r

ln2 = 24r

r = ln2/24 = about 0.029

A = Pe^029t where t = time in months, P = initial amount. A = future amount after time t

A = 20,000e^.29(4) = 20,000e^1.16

A = 20,000(3.19) =about 63,799 = population after 4 years

population doubles after 26/12 years = 13/6 years = about 2.17 years

4 years is less than double 2.17 years

so the population will be less than 20,000x 4 = 80,000

63,799 is in the appropriate range