Consider a population with constant relative birth and death rates and , respectively

Chapter 9, Problem 21

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Consider a population with constant relative birth and death rates and , respectively, and a constant emigration rate , where , , and are positive constants. Assume that . Then the rate of change of the population at time is modeled by the differential equation where (a) Find the solution of this equation that satisfies the initial condition (b) What condition on will lead to an exponential expansion of the population? (c) What condition on will result in a constant population? A population decline? (d) In 1847, the population of Ireland was about 8 million and the difference between the relative birth and death rates was 1.6% of the population. Because of the potato famine in the 1840s and 1850s, about 210,000 inhabitants per year emigrated from Ireland. Was the population expanding or declining at that time?