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Tumor growth The growth of cancer tumors may be modeled by the Gompertz growth equation. Let M(t) be the mass of a tumor, for t z 0. The relevant initial value problem is dM ( M(t)` -rM(t)ln ( ), M(0) = Mg. dt K where r and K are positive constants and 0 < M, < K. a. Show by substitution that the solution of the initial value problem is exp(-rt) M(t) = K K b. Graph the solution for M, = 100 and r = 0.05. c. Using the graph in part (b), estimate lim M(t), the limiting size of the tumor.

Tumor growth The growth of cancer tumors may be modeled by the Gompertz growth equation. Let M(t) be the mass of a tumor, for t z 0. The relevant initial value problem is dM ( M(t)` -rM(t)ln ( ), M(0) = Mg. dt K where r and K are positive constants and 0 < M, < K. a. Show by substitution that the solution of the initial value problem is exp(-rt) M(t) = K K b. Graph the solution for M, = 100 and r = 0.05. c. Using the graph in part (b), estimate lim M(t), the limiting size of the tumor.

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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Tumor growth The growth of cancer tumors may be modeled by the Gompertz growth equation. Let M(t) be the mass of a tumor, for t z 0. The relevant initial value problem is dM ( M(t)` -rM(t)ln ( ), M(0) = Mg. dt K where r and K are positive constants and 0 < M, < K. a. Show by substitution that the solution of the initial value problem is exp(-rt) M(t) = K K b. Graph the solution for M, = 100 and r = 0.05. c. Using the graph in part (b), estimate lim M(t), the limiting size of the tumor.
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 a tumor, for t z 0. The relevant initial value problem is dM ( M(t)` -rM(t)ln ( ), M(0) = Mg. dt K where r and K are positive constants and 0 < M, < K. a. Show by substitution that the solution of the initial value problem is exp(-rt) M(t) = K K b. Graph the solution for M, = 100 and r = 0.05. c. Using the graph in part (b), estimate lim M(t), the limiting size of the tumor.
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