-) Biologists stocked a lake with 500fish and estimated the carrying capacity (themaximal population for the fish of thatspecies in that lake) to be 5300. The numberof fish tripled in the first year.(a) Assuming that the size of the fishpopulation satisfies the logistic equation(1-*).dPdtKdetermine the constant k, and then solve theequation to find an expression for the size ofthe population after t years.kP(t)(b) How long will it take for the population toincrease to 2650 (half of the carryingсарacity)?It will takeyears.

Given equation, dPdt=kP(1-PK). (a) Carrying capacity is given K = 5300, Let us plug it in given…

-) Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5300. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation = kP (1-) dP = kP ( 1 dt K determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k P(t) (b) How long will it take for the population to increase to 2650 (half of the carrying сарacity)? It will take years.

-) Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5300. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation = kP (1-) dP = kP ( 1 dt K determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k P(t) (b) How long will it take for the population to increase to 2650 (half of the carrying сарacity)? It will take years.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

-) Biologists stocked a lake with 500
fish and estimated the carrying capacity (the
maximal population for the fish of that
species in that lake) to be 5300. The number
of fish tripled in the first year.
(a) Assuming that the size of the fish
population satisfies the logistic equation
(1-*).
dP
dt
K
determine the constant k, and then solve the
equation to find an expression for the size of
the population after t years.
k
P(t)
(b) How long will it take for the population to
increase to 2650 (half of the carrying
сарacity)?
It will take
years.

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