Question: Consider the differential equation as a model for a fish population, where is measured in weeks and is a constant. (a) Use a CAS to

Consider the differential equation as a model for a fish population, where is measured in weeks and is a constant.

(a) Use a CAS to draw direction fields for various values of c.
(b) From your direction fields in part (a), determine the values of c for which there is at least one equilibrium solution. For what values of does the fish population always die out?
(c) Use the differential equation to prove what you discovered graphically in part (b).
(d) What would you recommend for a limit to the weekly catch of this fish population?

dP 0.08P 1 1000 dt

Step by Step Solution

★★★★★

3.35 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a 1200 800 c 400 1200 800 400 40 c0 40 c 21 80 80 120 120 1200 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-D-E (89).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Consider the differential equation i+ 4 + 3y = n.

Consider the differential equation dx/dt = -(1 - x)4. Find the equilibrium, graph the rate of change as a function of x, and draw the phase-line diagram. Would you consider the equilibrium to be...

Consider the differential equation f + af + bf = g, where g is some fixed function. Assume that f0 is one solution of this equation, Find a solution to f + f - 6f = 2x3 - x2 - 2x.

I have literally posted the complete assignment information, can I please have some help with these two problems? MAT 375 Module Two Guided Activity: (Continuous) Dynamical Systems Our textbook has a...

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

(d) We say that a system is in equilibrium when the rate of change is equal to 0. For our model, that is equivalent to socing when L - 0.071 (1- 100, 000 - h - 0. Clearly, if L - 0 then we can have...

3 COLLEGE ALGEBRA - TRIGONOMETRY Business and Finance (MAT115) This course will start with a review of basic algebra (factoring, solving linear equations, and equalities, etc.) and proceed to a study...

1. Campus police are investigating a hit-and-run accident in which the driver of a late- model sports car has run down the statue of a popular mathematics professor. The accident took place at 8:00...

Can you please help me with Question 1 please? Much appreciated = RN (1-x) The implementation of a good harvesting policy for fisheries is crucial to ensure a sustainable population of fish. If (t)...

Using McDonalds Restaurant, evaluate the "current state" of the technology within the organization as it relates to people and processes of the business. Focus and report on: Identify types of...

a Proton transfer b-Lewis acid/base e-E2 elimination 1. 2. CH Submit Answer NOT d-S2 Nucleophilic substitution - Electrophilic aromatic substitution f-Carbonyl nucleophilic addn [Review Topic] "CH...

ISO 9002:1994 includes __________elements. a. 18 b. 21 c. 19 d. 20

The balance sheets of Roop Industries are shown below. The 12/31/2004 value of operations is $651 million and there are 10 million shares of common equity. What is the price per share? Balance...

The heat capacity at constant pressure of hydrogen cyanide is given by the expression Cp[J/(mol C)] = 35.3 + 0.0291T(C) (a) Write an expression for the heat capacity at constant volume for HCN,...

For an 85 wt% Pb-15 wt% Mg alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 600C (1110F), 500C (930F),...

Calculating Expected Returns A portfolio is invested 10 percent in Stock, 75 percent in Stock 3, - and 15 percent in Stock K. The expected returns on these stocks are 8 percent, 15 percent, and 24...

A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is obtained by rotating a parabola about a vertical axis. (a) If its height is 4 ft and the...

Rolling along across the machine shop at a constant speed of 4.25 m/s, a robot covers a distance of 17.0 m. How long does that journey take?

Calculate y'. 4 1 u y = ? + + 1

Differentiate. y = / + 1

Find the derivative of the function. y = 5

Riverton Mining plans to purchase or lease $435,000 worth of excavation equipment. If purchased, the equipment will be depreciated on a straight-line basis over five years, after which it will be...

1 - Warr Company is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC or negative, in both cases it...

Desreumaux Inc's stock has an expected return of 12.25%, a beta of 1.25, and is in equilibrium. If the risk-free rate is 5.00%, what is the market risk premium? 5.80% 5.95% 6.09% 6.25% 6.40% Question...