Tumor growth The growth of cancer tumors may be modeled by the Gompertz growth equation. Let M(t) be the mass of the tumor for t 2 0. The relevant initial value problem is ам M -аM In K' M(0) = Mo. dt where a and K are positive constants and 0 < Mo < K. M a. Graph the growth rate function R(M) = -aM In K assuming a = 1 and K = 4. For what values of M is the growth rate positive? For what value of M is the growth rate a maximum? b. Solve the initial value problem and graph the solution for a = 1, K = 4, and Mo = 1. Describe the growth pattern of the tumor. Is the growth unbounded? If not, what is the limit- ing size of the tumor? c. In the general equation, what is the meaning of K?
Tumor growth The growth of cancer tumors may be modeled by the Gompertz growth equation. Let M(t) be the mass of the tumor for t 2 0. The relevant initial value problem is ам M -аM In K' M(0) = Mo. dt where a and K are positive constants and 0 < Mo < K. M a. Graph the growth rate function R(M) = -aM In K assuming a = 1 and K = 4. For what values of M is the growth rate positive? For what value of M is the growth rate a maximum? b. Solve the initial value problem and graph the solution for a = 1, K = 4, and Mo = 1. Describe the growth pattern of the tumor. Is the growth unbounded? If not, what is the limit- ing size of the tumor? c. In the general equation, what is the meaning of K?
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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Transcribed Image Text:Tumor growth The growth of cancer tumors may be modeled by
the Gompertz growth equation. Let M(t) be the mass of the tumor
for t 2 0. The relevant initial value problem is
ам
M
-аM In
K'
M(0) = Mo.
dt
where a and K are positive constants and 0 < Mo < K.
Transcribed Image Text:M
a. Graph the growth rate function R(M) = -aM In
K
assuming a = 1 and K = 4. For what values of M is the
growth rate positive? For what value of M is the growth rate a
maximum?
b. Solve the initial value problem and graph the solution for
a = 1, K = 4, and Mo = 1. Describe the growth pattern of
the tumor. Is the growth unbounded? If not, what is the limit-
ing size of the tumor?
c. In the general equation, what is the meaning of K?
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