If the population of a country doubles in 60 years , in how many years will it be triple (treble) under the assumption that the rate of increase is proportional to the number of inhabitants ?

Explanation

Let P be the population of the country at time t.
`:. (dP)/(dt) propP`
`:. (dP)//(dt)=KP`
`:. (dP)/(P)=K*dt`
Integrating both sides,
`int (1)/P)*dP= K int dt`
`:. Llog P= Kt+c " "...(1)`
Let `P=P_(0)at t=0`
Substituting in (1)
`log P_(0)=K*0+c`
`c=log P_(0)`
`:. log_(P)=Kt+log P_(0)`
`:. log P-log P_(0)= Kt`
`:. log (P)/(P_(0))= Kt" "...(2)`
When `t=60 yers P= 2P_(0)`
`:. "log"(2P_(0))/(P_(0))= 60 K`
`K=(1)/(60)xxlog2` [ From (2)]
`K=(1)/(60)xx0*6912`
`:.` Equation (2) can be written as
`"log" (P)/(P_(0))=(0*9312)/(60)xxt " "....(3)`
Now, when `P= 3P_(0), t ?`
`:. "log" (3P_(0))/(P_(0))=(0*6912)/(60)xxt`
`:.log 3xx(60)/(0*6912)=t`
`:. t=1*0986xx(60)/(0*9312)`
`t=95*36` yrs.