# Differential Equations - Population Growth

Would anyone be able to go through some of the steps for these problems?

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

a) Write a differential equation which models the population of the state. Be sure to define all variables.

b) Solve the differential equation.

c) How long will it take for the population to reach 10,000,000?

d) Generate a graph which shows the long term (50 years) population projection of the state under these conditions.

2. Now in addition to the facts above, assume that people are moving out of the state at a constant rate of 60,000 people per year.

a) Write a differential equation which models the population of the state given this emigration.

b) Solve the differential equation.

c) Will the population ever reach 10,000,000? If so, when? If not, why not?

d) Generate a graph which shows the long term (50 years) population projection of the state under these conditions.

e) At what constant rate will people have to leave the state in order for the state to have a constant population?

## The Attempt at a Solution

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Would anyone be able to go through some of the steps for these problems?

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

a) Write a differential equation which models the population of the state. Be sure to define all variables.

b) Solve the differential equation.

c) How long will it take for the population to reach 10,000,000?

d) Generate a graph which shows the long term (50 years) population projection of the state under these conditions.

2. Now in addition to the facts above, assume that people are moving out of the state at a constant rate of 60,000 people per year.

a) Write a differential equation which models the population of the state given this emigration.

b) Solve the differential equation.

c) Will the population ever reach 10,000,000? If so, when? If not, why not?

d) Generate a graph which shows the long term (50 years) population projection of the state under these conditions.

e) At what constant rate will people have to leave the state in order for the state to have a constant population?

## The Attempt at a Solution

Have similar problems been formulated and/or solved in your course notes or your textbook? If so, why don't you start by setting up the problem in a similar way? In particular, what is stopping you from at least doing part of (a), viz., defining your variables and their units of measurement?

RGV