The population model given in (1) in Section 1.3dPdtP ordpdtkP(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 therate 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 amodel 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 ofproportionality for the birth and death rates are ki and k2 respectively. Use P for P(t).)8/6

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Answered: The population model given in (1) in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1700 fish. Absent constraints, the population would grow by 130% per year. If the starting population is given by po = 100, then after one breeding season the population of the pond is given by P1 = After two breeding seasons the population of the pond is given by P2 =
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1) The population (p) of a small community on the outskirts of a city grows rapidly over a 20- year period: t (time) P (population) 5 10 15 20 100 200 450 950 2000 As an engineer working for a utility company, you must forecast the population 5 years into the future in order to anticipate the demand for power. Use an exponential model and linear regression to make this prediction. Determine r?. Plot the data along with the curve.
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