a citys population was 10000 in 1980 and 13000 in 1990 assum

a city\'s population was 10,000 in 1980 and 13,000 in 1990. assuming an exponential growth rate of (dy/dt=ky), to the nearest thousand, estimate the cities population in 2000.

We have

dy/dt=ky ==> dy/y=kdt

Integrate both sides with respect to t to get

lny=kt+c₁ ==> y=Ce^kt

Now, use the given data to solve for k. Let t=# of years after 1980. Then at t=0, y=10,000 and clearly C=10,000. At t=10, y=13,000, so we can use this to solve for k. We get

13,000=10,000e^10k ==> 13/10=e^10k ==> ln(13/10)=10k ==> ln(13/10)/10=k.026236. Now, we see that the exact growth equation is

y=10,000e^.026236t

Plug in t=20 (20 years after 1980) to estimate the population in 2000. We get

y=10,000e^.026236*20=16,900

$a city\'s population was 10,000 in 1980 and 13,000 in 1990. assuming an exponential growth rate of (dy/dt=ky), to the nearest thousand, estimate the cities popu$

a citys population was 10000 in 1980 and 13000 in 1990 assum

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