We know that M(0)=10. What is M'(0)? (Use the differential equation with r=1 and k=100) Round your answer to the closest whole number.
We know that M(0)=10. What is M'(0)? (Use the differential equation with r=1 and k=100) Round your answer to the closest whole number.
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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We know that M(0)=10. What is M'(0)? (Use the
Transcribed Image Text:5. Hopefully your answer to the previous question included the word "slope." A nice way to
visualize solutions to differential equations is with a slope field. For any value of t and M, we
plug into right-hand side of the differential equation to get the slope, dM/dt, and indicate the
slope at that point in the t-M plane by a short line segment as shown in the figure below. In
this plot, r =1 and K = 100, and the horizontal axis is t and vertical is M.
M 120
100
80
60
40
MlO)=10->
0.0
1.0
2.0
3.0
4.0
5.0
6.0
ノ///ニ
20
Transcribed Image Text:In this activity we will look at how we can approximate solutions to differential equations without
actually solving them. We will consider a model for a tumor growth known as the Gompertz growth
function. Let M(t) > 0 be the mass of a tumor at timet2 0. The relevant differential equation is
dM
-rM In
K
dt
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