Question

Assuming that P≥0, a population is modeled by the differential equation

dP/dt = 1.4P(1- P/3400)

1. For what values of P is the population increasing?
**Answer (in interval notation)**:

2. For what values of P is the population decreasing?
**Answer (in interval notation)**:

3. What are the equilibrium solutions? **Answer (separate
by commas)**: P =

Answer #1

A function y(t) satisfies the differential
equation
dy
dt
= y4 − 11y3 + 24y2.
(a) What are the constant solutions of the equation? (Enter your
answers as a comma-separated list.)
y =
(b) For what values of y is y increasing? (Enter
your answer in interval notation.)
y
(c) For what values of y is y decreasing? (Enter
your answer in interval notation.)
y

Suppose that a population develops according to the following
logistic population model.
dp/dt=0.04p-0.0001p^2
What is the carrying capacity?
0.0001
400
10000
0.04
0.0025
What are the equilibrium solutions for the population model
?
P = 400 only
P = 0 and P = 10000
P = 0 and P = 400
P = 0 only
Using the population model , for what values of
P is the population increasing?
(0,400)
and
(0,10000)
and

A population P obeys the logistic model. It satisfies the
equation
dP/dt=(2/700)*P(7−P) for P>0
Assume that P(0)=2. Find P(53)

Differential Equations problem
Given the equation - dP / dt = kP(M - P) - h
where k, h, and M are constant real numbers and P is population
as a function of time t, with the initial condition P(0) = Po, find
the solution for P(t).
Show your work and enough steps so another student can
understand the solution.

Suppose that the certain population obeys the logistics
equation
dP / dt = 0.025·P ·(1−P / C)
where C is the carrying capacity. If the initial population P0 =
C/3, ﬁnd the time t∗ at which the initial population has doubled,
i.e., ﬁnd time t∗ such that P(t∗) = 2P0 = 2C/3.

The population P(t) of bacteria grows according to the logistics
equation dP/dt=P(12−P/4000), where t is in hours. It is known that
P(0)=700. (1) What is the carrying capacity of the model? (2) What
is the size of the bacteria population when it is having is fastest
growth?

a. Solve the following differential equation, where r and ω are
constant parameters: dP/ dt = r(1 − cos(ωt))P
b. Solve the following differential equation: y'(x) + 4xy(x) =
2xe^(−x^ 2)

A population ?(?) can be modeled by the differential equation
??/?? = 0.1? (1 − ?/400)
a. Find the equilibrium solutions and describe what each
solution means for this population.
b. Describe the behavior of the function when ? > 400.
Explain.
c. Describe the behavior of the function when 0 < ? < 400.
Explain.
d. Sketch at least one solution illustrating each of parts (b)
and (c) in the first quadrant below. Include the equilibrium
solutions in your...

Suppose that the population develops according to the logistic
equation dP/dt = 0.0102P - 0.00003P^2 where t is measured in days.
What is the P value after 10 days where A = (M-P(0)) / P(0)) if the
P(0) = 40? And P(0) = 20?

Suppose a population P(t) satisfies
dP/dt = 0.8P − 0.001P2 P(0) =
50
where t is measured in years.
(a) What is the carrying capacity?
______
(b) What is P'(0)?
P'(0) = ______
(c) When will the population reach 50% of the carrying capacity?
(Round your answer to two decimal places.)
_____yr
Please show all work neatly, line by line, and justify steps so
that I can learn.
Thank you!

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