Suppose a population function P(t) satisfies the following differential equation. P is measured in millions and t is in years. dP/dt = P(P − 10), (a) Sketch a slope field. (b) Identify the equilibrium solutions (constant solutions) and classify them as stable, unstable, or semi-stable equilibrium. (c) Sketch a solution that satisfies the initial condition P(0)= 6 . [Show asymptote, if there is one, and indicate the exact P value of the inflection point.] (d) Write a definite integral for computing the time that it takes for an initial population of 6 (millions) to decline to 0.5 (million.) [Hint: Separate the variables. Think of t as a function of P.]
Suppose a population function P(t) satisfies the following differential equation. P is measured in millions and t is in years. dP/dt = P(P − 10), (a) Sketch a slope field. (b) Identify the equilibrium solutions (constant solutions) and classify them as stable, unstable, or semi-stable equilibrium. (c) Sketch a solution that satisfies the initial condition P(0)= 6 . [Show asymptote, if there is one, and indicate the exact P value of the inflection point.] (d) Write a definite integral for computing the time that it takes for an initial population of 6 (millions) to decline to 0.5 (million.) [Hint: Separate the variables. Think of t as a function of P.]
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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Suppose a population function P(t) satisfies the following differential equation. P is measured in millions and t is in years.
dP/dt = P(P − 10),
(a) Sketch a slope field.
(b) Identify the equilibrium solutions (constant solutions) and classify them as stable, unstable, or semi-stable equilibrium.
(c) Sketch a solution that satisfies the initial condition
(d) Write a definite integral for computing the time that it takes for an initial population of 6 (millions) to decline to 0.5 (million.) [Hint: Separate the variables. Think of t as a function of P.]
(b) Identify the equilibrium solutions (constant solutions) and classify them as stable, unstable, or semi-stable equilibrium.
(c) Sketch a solution that satisfies the initial condition
P(0)= 6
. [Show asymptote, if there is one, and indicate the exact P value of the inflection point.](d) Write a definite integral for computing the time that it takes for an initial population of 6 (millions) to decline to 0.5 (million.) [Hint: Separate the variables. Think of t as a function of P.]
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