dN %3D dt = 0.25N(10 - N), N(0) = 2 (a) %3D where N is measured in 100's. Analyze the behavior of this differential equation as follows. b. Obtain a slope field plot of this differential equation. Briefly analyze the slope field plot. Compare it to your qualitative plot in part (a) above. c. Solve this differential equation using the separation of variables technique. Plot the solution over the interval of time from [0, 10]. How does your actual solution compare to the qualitative graphical solution?

dN %3D dt = 0.25N(10 - N), N(0) = 2 (a) %3D where N is measured in 100's. Analyze the behavior of this differential equation as follows. b. Obtain a slope field plot of this differential equation. Briefly analyze the slope field plot. Compare it to your qualitative plot in part (a) above. c. Solve this differential equation using the separation of variables technique. Plot the solution over the interval of time from [0, 10]. How does your actual solution compare to the qualitative graphical solution?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

5. The Spread of a Contagious Disease. Consider the following ordinary differential
equation model for the spread of a communicable disease:
w
dN
= 0.25N(10 – N), N(0) = 2
dt
(a)
|
where N is measured in 100's. Analyze the behavior of this differential equation as
follows.
b. Obtain a slope field plot of this differential equation. Briefly analyze the slope field
plot. Compare it to your qualitative plot in part (a) above.
c. Solve this differential equation using the separation of variables technique. Plot the
solution over the interval of time from [0, 10]. How does your actual solution compare
to the qualitative graphical solution?

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