Question

1. The population of a town was 7420 in 2010. The population grows at a rate of 2.3% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (b) Estimate the population of the town in 2022. Show your work.​

Answer 1

Hello,

I hope you and your family are doing well!

(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).

Substituting the given values into the equation gives us:

P(t) = 7420 * 1.023^t

This is the equation that estimates the population t years after 2010.

(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:

P(12) = 7420 * 1.023^12

Calculating this gives us:

P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45

So the estimated population of the town in 2022 is approximately 9593

Happy to help!