Exponential equation

Question

There are 100,000 people and it increases 15% every year. Write an exponential equation for this information.

Answer 1

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

The general form of an exponential growth equation that you can use here is

y = a(1 + r)^t

so from there it’s just a matter of plugging in the underlying values that we know

a = initial population = 100,000 and

r = annual growth rate = 15% = 0.15

putting that together gives

y = 100000(1 + 0.15)^t

y = 100000(1.15)^t

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

P(t) will be the number of people as a function of the number of years t.

100,000 is the initial amount of people.

15% or 0.15 is the growth rate.

P(t) = 100,000(1 + .15)^t

or P(t) = 100,000(1.15)^t