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POPULATION PROBLEM

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1 ) suppose that country's population at any time t grows in accordance with rule dp/dt=kp+l where p denotes the population at anytime t , k is a positive constant reflecting the natural grow rate of the population, and l is a constant giving the constant rate of the immigration in to the country
a) If the population of the country at time t=0 is Po, find and expression for the population at any time t
b) The population of US in the year 1980 (t=0) was 226.5 million. Suppose natural grow rate is %0.8 annually (k=0.0008) and net immigration is allowed rate of 0.5 million per year (l=0.5) what will the population be at 2010 (answer with decimal points)

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Solution Summary

The expert examines population growth and immigration. The function dp/dt=kp+l where p denotes the population at anytime t , k is a positive constant reflecting the natural grow rate of the population, and l is a constant giving the constant rate of the immigration in to the country is analyzed. A complete, neat and step-by-step solution is provided.

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(a) dP/dt = kP + I

dP/(kP + I) = dt

Let kP + I = u then k dP = du and so dP = du/k

(du/k) / u = dt

du/u = k dt

Upon ...

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