Math Question asking about population in College Algebra

Question

The population of a city (in millions) at time t (in years) is P(t)=2.3e^0.004t, where t=0 is the year 2000.

When will the population double from its size at t=0

Answer 1

Hello, thank you for taking the time to post your question!

I would estimate the doubling time using the Rule of 70 … it’s a simple formula that allows you to determine how long it will take a value to double when it’s growing at a constant annual percentage rate. In this case we have

Doubling Time = 70 / 0.004*100 = 70/0.4 = 175 years, meaning that it will take around 175 years for the value to double here. That makes the year

2000 + 175 = 2175 when the population will have doubled

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

2 = exp(0.004t)

ln 2 = 0.004t

ln 2 / 0.004 = t

t = 173.28679513998632735430803036454

It will happen sometime in March 2173