Question

A population of a certain city increases exponentially at a rate of 5.7%. Initially, it is 1.84 million. After how many years will the population reach 3.21 million?

Answer 1

t = 10.0 years

It will take 10 years for the population to reach 3.21 million

Explanation:

Given;

Initial population P = 1.84 million

Final population F = 3.21 million

Rate r = 5.7% = 0.057

time t = ?

The exponential growth can be expressed as;

F = P(1+r)^t

We need to make t the subject of formula;

F/P = (1+r)^t

Taking natural logarithm of both sides;

ln(F/P) = tln(1+r)

t = ln(F/P) ÷ ln(1+r)

Substituting the given values;

t = ln(3.21/1.84) ÷ ln(1+0.057)

t = 10.0 years

It will take 10 years for the population to reach 3.21 million