Answer to Question #349168 in Differential Equations for Un Bunthim

Question #349168

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?


1
Expert's answer
2022-06-09T08:11:54-0400
"\\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.



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