Question

Assuming your population of 150 people grew steadily by 5% each year for five years and then disaster struck in the form of earthquakes and tsunamis! A quarter of your population died. How long will it take to regain your lost population? Use an exponential or logarithmic equation and graph to show your results. Round the years to two decimal places.

Answer 1

Solution :

Initially population contains 150 people. It is growing steadily with 5% each year for five years. The exponential growth of this population is given by,

pn = 150*exp(0.05*n) ; where pn= population after "n" number of years.

Then after 5 years a disaster struck in the form of earthquakes and tsunamis. And a quarter of this population died.

So after 5 years the population will be, p5 = 150*exp(0.05*5) = 150*exp(0.25) = 192.60.

A quarter of this population died and remains with population (1 - 0.25)*192.60 = 0.75*192. 60 = 144.45

Let us assume it require n0 years to regain the lost population from the population 144.45 to 192.60.

This gives, 144.45*exp(0.05*n0) = 192.60. Solving this equation for "n0" we will get, n0 = ln(192.60/144.45) / 0.05 = 5.7536   5.75.

And hence it will take 5.75 years to regain your lost population.