Let the population of living fish at time t (years) be denoted by x(t) (tonnes). An initial quantity of x0 tonnes of fish will be put into the lake at time t = 0. The net rate of change of the fish population in tonnes of fish per year is dx - = 0.5x = x² - f, x(0) = = x0 dt where xo) and f are non-negative constants and f represents the fish-harvesting rate. (a) Taking f = 0, write down the resulting differential equation stating clearly the solution method used.

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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Let the population of living fish at time t (years) be denoted by x(t) (tonnes). An initial
quantity of x0 tonnes of fish will be put into the lake at time t = 0. The net rate of change of
the fish population in tonnes of fish per year is
dx
-
= 0.5x = x² - f,
x(0) =
= x0
dt
where xo) and f are non-negative constants and f represents the fish-harvesting rate.
(a) Taking f
=
0, write down the resulting differential equation
stating clearly the solution method used.
Transcribed Image Text:Let the population of living fish at time t (years) be denoted by x(t) (tonnes). An initial quantity of x0 tonnes of fish will be put into the lake at time t = 0. The net rate of change of the fish population in tonnes of fish per year is dx - = 0.5x = x² - f, x(0) = = x0 dt where xo) and f are non-negative constants and f represents the fish-harvesting rate. (a) Taking f = 0, write down the resulting differential equation stating clearly the solution method used.
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