I don’t understand how to go about solving for part b of these problems, a Step

Question

I don’t understand how to go about solving for part b of these problems, a Step by step procedure would be helpful in a certain city is 8% per year, and the death rate is 3% per year. Also, there is a net movement t the city at a steady rate of 1000 people per year. Let N f(t) be the city's population at 5) The birt h rate time t. Nrite a differential equation satisfied by N. (b) Determine if there is a size at which the population would remain constant. 6) The birth rte in a certain city is 5% per year, and the death rate is 3% per year. Also, there is a net movement of population in to the city at a steady rate of 2000 people per year. Let N f(t) be the city's population at time t. Write a differential equation satisfied by N (b) Determine if there is a size at which the population would remain constant.

Explanation / Answer

5) a) Let N=f(t) be the city’s population at time t.

So we can write the differential equation as

dN/dt=0.08N-0.03N-1000

dN/dt=0.05N-1000

Which is the required differential equation.

b) The population would remain constant if dN/dt=0,

So, substituting dN/dt=0 in the equation and solving for N we get,

0=0.05N-1000

0.05N=1000

N=1000/0.05

N=20000

So, when N=20000, the population of the city would remain constant.

6) a) The differential equation for this is,

dN/dt=0.05N-0.03N-2000

dN/dt=0.02N-2000

Which is the required differential equation.

b) The population would remain constant if dN/dt=0,

So, substituting dN/dt=0 in the equation and solving for N we get,

0=0.02N-2000

0.02N=2000

N=2000/0.02

N=100000

So, when N=100000, the population of the city would remain constant.

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