A town has a population of 4000 and grows at 3.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 9000?

Answer 1

Hi there! I'd love to help you out.

When working with population growth we use the following formula:

A = Pe^(rt) where P is your initial population, e is Euler's number, r is your rate of increase, t is time, and A is your new population.

Now we know our initial population (P) is 4000, our rate of growth (r) is .035, and our new population is 9000. We will be solving for t:

9000 = 4000e^(.035t) 1. Divide by 4000

/4000 /4000

ln2.25 = ln[e^(0.35t)] 2. Take the natural log of both sides to get rid of the "e"

ln(2.25) = 0.35t ln(e) 3. Use the law of natural logs to bring the exponent in front

ln(2.25) = 0.35t 4. The ln and e cancel each other

/0.35 /0.35 5. Divide by 0.35

2.317 = t

Our problem wants us to round to the nearest tenth so our final answer would be 2.3 year. I hope this explanation was thorough and answered all of your questions. Please don't hesitate to reach out with any additional questions you may have. Learn on! :)