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# Population growth differential equation.

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The birth rate in a state is 2% per year and the rate is 1.3% per year. The population of the state is now 8,000,000.

a) At what rate are babies being born in the state now? with units

b) At what rate are people dying in the state now?

c) Write a differential equation that the population of the state satisfies. include the terms

d) Solve that differential equation

e) How many years till population gets to 10,000,000

f) Does the population have a steady rate? Explain

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#### Solution Preview

Please see the attached file.

Let define the population birth rate as  and the unit is births per person per year. Here =2% or 0.02
Let us define the population death rate as  and the unit is deaths per person per year. Here =1.3% or 0.013

If the population at time t is N(t), then the number of births will be N(t).

1. If N(t)=8,000,000 then the rate of births is:

2. At the same year the ...

#### Solution Summary

The population growth for differential equations are provided. The rate babies are being born in the state is determined.

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