Question

Find the population of a city after $2$ years, which is at present $12$ lakh, if the rate of increase is $4$.

Answer 1

Let the population be $P$

$\frac{dP}{dt}=4⟹\int dP=\int 4dt⟹P=4t+c$

At $t=0,P=12⟹c=12$

Now $P=4t+12$

At $t=12,P=4\times 2+12=20$

Hence, population after $2$ years$=20$ lakh.