Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
See similar textbooks
icon
Related questions
Question
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS