Help with my math HW

Question

A town in the Midwest has been experiencing a steady population decline of 3.75% per year for the past decade. If there were 45,470 residents in the year 2011 and the trend continues, what will the population be in the year 2031? Use the appropriate numerical expression to arrive at your response, and round your answer to the nearest person.

Answer 1

This is a great examples of exponential decay! When presented with a problem involving population growth or decay, use the following equation:

Decreasing population ----> y = a (1 - r)^t Increasing population----> y = a (1 + r)^t

In these forulas "a" is the initial population, "r" is the rate of increase or decrease (always put your percent in as a decimal), and "t" is time. In this example, we know the population is decreasing at a rate of 3.75% with an initial population of 45,470. We want to know what the population will be 20 years from now in the year 2031. So:

a = 45,470 r = .0375 t = 20

Now just plug it into the decreasing population formula:

y = 45,470 ( 1 - .0375)²⁰

Plug it all into your calculator and you should have your answer.

Answer 2

Population P can be expressed as 43,750 ( 1 + .0375 ) ²⁰ = 91,356.6 or rounded 91,357