Suppose a population function P(t) satisfies the following differential equation. P is measured in millions and t is in
Posted: Tue May 10, 2022 5:54 pm
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.]
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.]