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population model given in (1) in Section 1.3 (1) fals to take death into consideration, the growth rate equels the birth rate. In enother model of a chenging population of a communty itis essumed that the rate et which the population changes is a net rete-that is, the dference between the rate of births and the rate of deaths in the community. Determine a model for the population P(e) both the birth rate and the death rate are proportional to the population present et time > 0. (Assume the constants ef proportionality for the birth and death rates are k, and k, respectively. Use Pfor Pe)-)

population model given in (1) in Section 1.3 (1) fals to take death into consideration, the growth rate equels the birth rate. In enother model of a chenging population of a communty itis essumed that the rate et which the population changes is a net rete-that is, the dference between the rate of births and the rate of deaths in the community. Determine a model for the population P(e) both the birth rate and the death rate are proportional to the population present et time > 0. (Assume the constants ef proportionality for the birth and death rates are k, and k, respectively. Use Pfor Pe)-)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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The population model given in (1) in Section 1.3 (1) fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net rate-that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t> 0. (Assume the constants of proportionality for the birth and death rates are k, and k, respectively. Use P for P(t).)
Transcribed Image Text:The population model given in (1) in Section 1.3 (1) fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net rate-that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t> 0. (Assume the constants of proportionality for the birth and death rates are k, and k, respectively. Use P for P(t).)
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