Answer to Question #349168 in Differential Equations for Un Bunthim

Question

There are 10000 people living in a certain city. Suppose that the rate of population growth in the city is proportional to the number of inhabitants. Suppose that 20% of the original amount increase in 20 years, how much will the population in the city after 40 years?

Answer 1

$\dfrac{dy}{dt}=ky$ $y(t)=y(0)e^{kt}$

Given $y(0)=10000, y(20)=1.2y(0).$

Then

$y(20)=y(0)e^{20k}=1.2y(0)$

$e^{20k}=1.2$

$y(40)=y(0)e^{k(40)}$

$y(40)=y(0)(1.2)^2$

$y(40)=1.44y(0)$

$y(40)=1.44(10000)$

$y(40)=14400$

There will be 14400 people in a city after 40 years.