Question

The population of a country doubles in 25 years. How many years will it take for the population to be FOUR times as much as the initial amount? Assume that rate of increase is proportional to the number of inhabitants.

Answer 1

We can model the problem with the equation

$P(t)=p$

where

t= times

p = population

if the country doubles the population in 25 years

$P(25)=2p$

in other 25 five years the population doubles again

$P(50)=2(2p)$$P(50)=4p$

We are request to find the time (t) where the initial population (p) increase 4times

then given the equation

$P(50)=4p$

the initial population will take 50years to be FOUR times as much as the initial amount