This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of an unso- phisticated population (such as alligators). Show that this equation can be rewritten in the form dx/dt = k(x – H)(x – K), where H = (M + VM² + 4h/k) > 0, (~- K = ( M M² + 4h/k ) < 0.

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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This problem deals with the differential equation dx/dt
kx(x – M) – h that models the harvesting of an unso-
phisticated population (such as alligators). Show that this
equation can be rewritten in the form dx/dt = k(x –
H)(x – K), where
H = (M + VM² + 4h/k) > 0,
(~-
K = ( M
M² + 4h/k
) < 0.
Transcribed Image Text:This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of an unso- phisticated population (such as alligators). Show that this equation can be rewritten in the form dx/dt = k(x – H)(x – K), where H = (M + VM² + 4h/k) > 0, (~- K = ( M M² + 4h/k ) < 0.
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