Explanation Given information: A function is given by p ( t ) = 1 r e − t r on the interval [ 0 , ∞ ) . Formula used: The indefinite integral can be calculated as shown below. ∫ e − a t d t = e − a t − a + C Calculation: Let us consider the given function. p ( t ) = 1 r e − t r Now let us evaluate the integral ∫ 0 ∞ p ( t ) d t as follows: ∫ 0 ∞ p ( t ) d t = ∫ 0 ∞ 1 r e − t / r d t = lim A → ∞ ∫ 0 A

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 8.1, Problem 12E

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That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.

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Chapter 8.1, Problem 11E

Chapter 8.1, Problem 13E

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The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

Find the indefinite integral. Check Answer: 7x 4 + 1x dx

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Chapter 8 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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That p ( t ) satisfies the condition ∫ 0 ∞ p ( t ) d t = 1 for all r > 0 .

Solution Summary: The author explains that p(t) satisfies the condition for the function.

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To show:

That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.

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Chapter 8 Solutions

That p ( t ) satisfies the condition ∫ 0 ∞ p ( t ) d t = 1 for all r &gt; 0 .

Solution Summary: The author explains that p(t) satisfies the condition for the function.

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To show: That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.

Want to see the full answer?

Chapter 8 Solutions

That p ( t ) satisfies the condition ∫ 0 ∞ p ( t ) d t = 1 for all r > 0 .

To show:

That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.