Question

SHOW WORK:

The population of a town is decreasing at a rate of 2.5% per year. If the population in 2000 was 28,000, what is the expected population in 2015 of this rate of decrease continues?

Answer 1

Expected population in 2015: 19,152.58 or 19,000 people

Explanation:

Given the decreasing rate of 2.5% per year, and a population of 28,000 in the year 2000:

We can solve for the rate of decrease by using the formula:

`A = a(1 - r )^(t)`

where:

A = population by year 2015

a = initial population (in year 2000) = 28,000

r = rate of change (decrease by 2.5% annually or 0.025)

t = time (in number of years) = 15

Plug in these given values into the formula:

`A = a(1 - r )^(t)`

`A = 28,000(1 - 0.025 )^(15)`

`A = 28,000(0.975)^(15)`

A = 28,000(0.684)

A = 19,152.58 or about 19,000 people in 2015