The logistic model of growth takes the general form,y=k/1+be^-atwhere k, a and b are positive constants.(a) Find an expression for dy/dt and deduce that the gradient is positive.(b) Find an expression for d^2y/dt^2 and deduce that the graph is convex when t < (ln b)/a and concave when t > (ln b)/a.(c) State the coordinates of the point where the graph intercepts the y axis, and describe the behaviour of the graph as t ➜∞.(d) Sketch a graph of this logistic function. The logistic model of growth takes the general form,ky :1+ be-atwhere k, a and b are positive constants.(a) Find an expression for dy/dt and deduce that the gradient is positive.(b) Find an expression for dy/df and deduce that the graph is convex when t < (In b)laand concave when t> (In b)la.(c) State the coordinates of the point where the graph intercepts the y axis, and describethe behaviour of the graph as t→ 0.(d) Sketch a graph of this logistic function.

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Description: The logistic model of growth takes the general form,y=k/1+be^-atwhere k, a and b are positive constants.(a) Find an expression for dy/dt and deduce that the gradient is positive.(b) Find an expression for d^2y/dt^2 and deduce that the graph is convex

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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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The logistic model of growth takes the general form,
y=k/1+be^-at
where k, a and b are positive constants.
(a) Find an expression for dy/dt and deduce that the gradient is positive.
(b) Find an expression for d^2y/dt^2 and deduce that the graph is convex when t < (ln b)/a and concave when t > (ln b)/a.
(c) State the coordinates of the point where the graph intercepts the y axis, and describe the behaviour of the graph as t ➜∞.
(d) Sketch a graph of this logistic function.

The logistic model of growth takes the general form,
k
y :
1+ be-at
where k, a and b are positive constants.
(a) Find an expression for dy/dt and deduce that the gradient is positive.
(b) Find an expression for dy/df and deduce that the graph is convex when t < (In b)la
and concave when t> (In b)la.
(c) State the coordinates of the point where the graph intercepts the y axis, and describe
the behaviour of the graph as t→ 0.
(d) Sketch a graph of this logistic function.

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