Question

A mathematical model for population growth over short intervals is given by PequalsUpper P 0 e Superscript rt​, where Upper P 0 is the population at time tequals​0, r is the continuous compound rate of​ growth, t is the time in​ years, and P is the population at time t. How long will it take a​ country's population to triple if it continues to grow at its current continuous compound rate of 0.86​% per​ year?

Answer 1

12.8 years

Explanation:

Put the given numbers into the model and solve for t.

`3P_0=P_0e^(.086t)\\\\3=e^(.086t) \qquad\text{divide by $P_0$}\\\\ln(3)=.086t \qquad\text{take the natural log}\\\\(ln(3))/(.086)=t\approx 12.77`

It will take about 12.77 years for the population to triple at the current growth rate.