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 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Sketch the equilibrium solution M(t) = K = 100 from part 1. into the plot. Does it agree with the plotted slopes/directions at every point it passes through? 20
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 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Sketch the equilibrium solution M(t) = K = 100 from part 1. into the plot. Does it agree with the plotted slopes/directions at every point it passes through? 20
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.
%3D
6.
M 120
100
80
60
0.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Sketch the equilibrium solution M(t) = K = 100 from part 1. into the plot. Does it agree
with the plotted slopes/directions at every point it passes through?
%3D
40
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 timet > 0. The relevant differential equation is
dM
dt
-rM ln
K
where r and K are positive constants.
1. Verify that the differential equation has a constant solution when M = K. (You want to show
dM
that
is equal to 0. This is called an equilibrium solution.)
dt
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
