A population of fish is living in an environment with limited resources. This environment canonly support the population if it contains no more than M fish (otherwise some fish wouldstarve due to an inadequate supply of food, etc.). There is considerable evidence to supportthe theory that, for some fish species, there is a minimum population m such that the specieswill become extinct if the size of the population falls below m. Such a population can bemodelled using a modified logistic equation:dP=(1-)(-)mdtM 10, 000, draw a direction field and useFor the case where k = 1, M = 100, 000 and m =it to sketch several solutions for various initial populations. What are the equilibriumsolutions?One can show thatk(М-т),M(Po – m)e(Ро — т)еt.т(Ро — М)MP(t) =k(М-т)tM– (Po – M)is a solution with initial population P(0) = Po. Use this to show that, if P(0) < m, thenthere is a time t at which P(t) = 0 (and so the population will be extinct).

In the given problem it is given a differential equation in P. Also, there are values for k, M and m…

Answered: 10, 000, draw a direction field and use…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Jackie and Christine are racing again! We only get some discrete data this time, but we can find the details through calculation! 3 minutes after the race starts, Jackie is 12 miles away from the starting point, and Christine is 27 miles ahead of Jackie. 13 minutes after the race starts, Jackie is 52 miles away from the starting point, but now Christine is only 17 miles ahead from Jackie. Assume they are going at a constant speed. (a) Present their movement on the xy-plane, where the x- and y-axis represent the time since the race starts and their distances from the starting point respectively. Label the four points clearly. (b) Find the speed of Christine and Jackie. You may use the unit “miles per minute” or, if you are comfortable with unit conversion, “miles per hour.” (c) Is anyone given a head start? If so, who is that and how far was that? (d) How far is Jackie from the starting point when he catches up with Christine?
3. At a carnival, there is a single player game called the High Striker. Here is how the game works: • A player takes a mallet and swings it at a target that is located at the base of the High Striker. • For every swing that a player takes, they receive a score that is directly proportional to the force of that swing. • If the player's score on any given swing is greater than y (where y > 0), then the player wins a prize. • A player may swing as many times as they like during the game. • There is no limit on the number of prizes that a player can win during the game. Players are classified as either fit with probability p or unfit with probability 1 – p. Players are also classified as either competitive or non-competitive. A fit player has probability cf of being competitive, whereas an unfit player has probability cu of being competitive. On any given swing, the score received by a fit player follows a U(0, m) distribution, whereas the score received by an unfit player follows a U(0,…
Suppose that y (t) =A t e +B is a solution to y"-3y'=4y =-5e-4, where {A, B, a} are constant numbers. Then A is equal to: A. -1 В. 4 С. 1 D. -0.5
Consider the initial value problem: 2t a'= ()+ a0), a(1) = (-). 2t2 t+a Suppose we know that æ(t) = (a,) is the unique solution to this initial value problem. Find the constants a and B and the vector function g(t). 3t2 + B a = B = g(t) =
9
y e-2 is a solution to the following ODE:y" - 2/ - 8y = 0. Use Reduction of Order to find a 2nd linearly independent solution Step 1: Let y Select] Then y'Select] [Select] Step 2: Substitute y, y', and y" into the ODE and simplify to get Step 3: Reduce the Order. Let w = u' [Select] Step 4: Solve the equation for w. Step 5: Solve for u. Step 6. Identify the two linearly independent solutions. 2 was given as one solution. A second linearly independent solution is Select]
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The same disease is spreading through two populations, say Pi and P2, with the same size. You may assume that the spread of the disease is well described by the SIR model. dSa - BaSaIa dt dla - dt dRa YaIa dt with Sa(0) + I.(0) + R.(0) = N where N denotes the fixed population size. The subscript a identifies the population P or P2. For example, if a = 1, the variables are related to P1. Assume that S1 (0) = S2 (0) and I1(0) = I½(0) and that no interventions such as quarantine or vaccination have been implemented. If the difference in the spread of the disease is due only to the poor over-all health of a population, which population has the best over-all health of the two populations? - Susceptible Population 1 - Susceptible Population 2 700 600 500 400 300 200 100 10 15 20 t P1. P2. Susceptible
Explain the determine grren

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