24. Suppose that a population can be accurately modeled by the logistic equation dp di =0.4p (1-). (Note that the growth-rate parameter is 0.4 and the carrying capacity is 30.) Suppose that, at time / 5, a disease is introduced into the population that kills 25% of the population per year. To adjust the model, we change the differential equation to 0.4p (1-30 for 0 <1 < 5; dp dr 0.4p (1-) - 0.25p for t > 5. (a) Sketch the slope field for this equation using HPGSolver. (b) Using the slope field, sketch the graphs of a few representative solutions to this equation. (c) Find formulas for the solutions of this equation for initial conditions p(0) = 30 and p(0) = 20. (d) In a few sentences, describe the behavior of the solutions with initial conditions p(0) = 30 and p(0) = 20. (You can use either the sketches from the slope field or the formulas, but give a qualitative description of the solutions.)
24. Suppose that a population can be accurately modeled by the logistic equation dp di =0.4p (1-). (Note that the growth-rate parameter is 0.4 and the carrying capacity is 30.) Suppose that, at time / 5, a disease is introduced into the population that kills 25% of the population per year. To adjust the model, we change the differential equation to 0.4p (1-30 for 0 <1 < 5; dp dr 0.4p (1-) - 0.25p for t > 5. (a) Sketch the slope field for this equation using HPGSolver. (b) Using the slope field, sketch the graphs of a few representative solutions to this equation. (c) Find formulas for the solutions of this equation for initial conditions p(0) = 30 and p(0) = 20. (d) In a few sentences, describe the behavior of the solutions with initial conditions p(0) = 30 and p(0) = 20. (You can use either the sketches from the slope field or the formulas, but give a qualitative description of the solutions.)
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please solve "c" and "d" part, not "a" and "b" part.
Transcribed Image Text:24. Suppose that a population can be accurately modeled by the logistic equation
dp =04p (1- 30)
dt
(Note that the growth-rate parameter is 0.4 and the carrying capacity is 30.) Suppose
that, at time i = 5, a disease is introduced into the population that kills 25% of the
population per year. To adjust the model, we change the differential equation to
0.4p (1-P
for 0<1 < 5;
dp
30.
dr
0.4p (1 -)- 0.25p fort > 5.
(a) Sketch the slope field for this equation using HPGSolver.
(b) Using the slope field, sketch the graphs of a few representative solutions to this
equation.
(c) Find formulas for the solutions of this equation for initial conditions p(0) = 30
and p(0) = 20.
(d) In a few sentences, describe the behavior of the solutions with initial conditions
p(0) = 30 and p(0) = 20. (You can use either the sketches from the slope field
or the formulas, but give a qualitative description of the solutions.)
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Step 1: Given
VIEWStep 2: P(t) when t = [0,5)
VIEWStep 3: p(t), When t= 0, p(0) =20
VIEWStep 4: p(t), When t= 0, p(0) =30
VIEWStep 5: P(t) when t > 5.
VIEWStep 6: P(t) for t> 5 For case a) when t = 0 , p(0) = 20.
VIEWStep 7: P(t) for t> 5 For case b) when t = 0 , p(0) = 30.
VIEWStep 8: P(t) for case (a)
VIEWStep 9: For case b)
VIEW
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