5-3 Practice Problems

Question

Suppose a city with population

300,000

has been growing at a rate of

3​%

per year. If this rate​ continues, find the population of this city in

24

years.

Answer 1

Hello Savannah,

Since there's a 3% growth every year, it means that to find the population from one year to the next, you would multiply by (100% + 3%) or 103%, which is 1.03 as a decimal

The formula that would represent the population size is: P(t) = P₀ * (1.03)^t

where P₀ is the initial population, P(t) is the final population, and t is the time it takes for the population to equal P(t)

You're asked to find the population in 24 years, so P(24):

P(24) = 300000 * (1.03)²⁴

P(24) = 300000• (2.0327941) = 609,838 ---> the population of this city in 24 years would be 609,838

Cheers.