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

Answer:

  12.8 years

Step-by-step explanation:

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

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

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