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2. Another equation that has been used to model population growth is the Gompertz equation dy/dt = ry ln(K/y), where r and K are positive constants. (a) Sketch the graph of f(y) versus y, find the critical points, and determine whether each is asymptotically stable or unstable. (b) For 0 ≤ y ≤ K, determine where the graph of y versus t is concave up and where it is concave down. (c) For each y in 0 ≤ y ≤K, show that dy/dt, as given by the Gompertz equation, is never less than dy/dt, as given by the logistic equation.

2. Another equation that has been used to model population growth is the Gompertz equation dy/dt = ry ln(K/y), where r and K are positive constants. (a) Sketch the graph of f(y) versus y, find the critical points, and determine whether each is asymptotically stable or unstable. (b) For 0 ≤ y ≤ K, determine where the graph of y versus t is concave up and where it is concave down. (c) For each y in 0 ≤ y ≤K, show that dy/dt, as given by the Gompertz equation, is never less than dy/dt, as given by the logistic equation.

Advanced Engineering Mathematics
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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2. Another equation that has been used to model population growth is the Gompertz equation dy/dt = ry ln(K/y), where r and K are positive constants. (a) Sketch the graph of f(y) versus y, find the critical points, and determine whether each is asymptotically stable or unstable. (b) For 0 ≤ y ≤ K, determine where the graph of y versus t is concave up and where it is concave down. (c) For each y in 0 ≤ y ≤ K, show that dy/dt, as given by the Gompertz equation, is never less than dy/dt, as given by the logistic equation.
Transcribed Image Text:2. Another equation that has been used to model population growth is the Gompertz equation dy/dt = ry ln(K/y), where r and K are positive constants. (a) Sketch the graph of f(y) versus y, find the critical points, and determine whether each is asymptotically stable or unstable. (b) For 0 ≤ y ≤ K, determine where the graph of y versus t is concave up and where it is concave down. (c) For each y in 0 ≤ y ≤ K, show that dy/dt, as given by the Gompertz equation, is never less than dy/dt, as given by the logistic equation.
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