If the poplulatin of a particular country is growing at 28 c

If the poplulatin of a particular country is growing at 2.8% compounded continously, how long will it take the population to quadruple? (round up to nearest years)

Solution

As for continuous growth, the ratio of the final to the initial population is given by

P/Po = e^(rt)

where r = 2.8% = 0.028, then, if P/Po = 4 [quadruple],

4 = e^(0.028t)

Taking the ln of both sides,

ln (4) = 0.028t

t = ln(4) / 0.028 = 49.5105129 --> 50 YEARS [ANSWER]