(4) Consider the equationdr(t)dt=(205+0.1)et,with initial condition z(0) = 1.0. Find an approximate solution to (1) by evolving the systemfrom t = 0 tot = 1 with a single 2nd-order Runge-Kutta step. Give a rough quantitative estimateof the discretisation error by comparing two different methods or two different step sizes.=

Given differential equation is dxtdt = x0.5 +0.1e-t. Initial condition:- x0=1.0 Find an approximate…

Answered: (4) Consider the equation dz(t)…

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.CR: Chapter 11 Review

Problem 12CR

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Consider the system dx x – xy – x² dt ху — 2у dt where x and y denote the sizes of two interacting populations. (1.1) How does the x species and the y species, respectively, behave in the absence of the other species? (1.2) Describe the type of interaction between the two species (e.g. competition, predator/prey, etc.) (1.3) Draw the phase diagram and use it to predict the outcome of the system if initially xo = 2, Yo = 2.
Consider the system dx х — ху — 22 dt dy ху — 2у dt where x and y denote the sizes of two interacting populations. (1.1) How does the x species and the y species, respectively, behave in the absence of the other species? (1.2) Describe the type of interaction between the two species (e.g. competition, predator/prey, etc.) (1.3) Draw the phase diagram and use it to predict the outcome of the system if initially xo = 2, Yo = 2. ||
Find the value of dt 2 5. at the point (0, -1) if xy + y = 1
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
Find an explicit solution of the given initial value problem using separation of variables.
the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows: dA/dt=2A=0.01AL dL/dt=-0.5L+0.0001AL a) find the two critical points of the predator-prey equations b) use the chain rule to write dL.dA in terms of L and A c) suppose that at time t=0, there are 1000 aphids and 200 ladybugs, use the Bluffton university slope field generator to graph the slope for the system and the solution curve. let 0 be less than or equal to A who is less than or equal to 15000 and 0 is less than or equal to L which is less than or equal to 400.
4) A toxic chemical accidentally released into the environment from a metal processing plant degrades according to the law dQ dt -0.04Q where t is measured in years. If the initial leak is of 60kg, a. Use the separation of variables method to find the amount remaining at any given time. b. Prove that the general solution found above can also generated using the integrating factor method. c. Find the amount remaining after 10 years.
Use an appropriate form of the chain rule to find dz/dt (Please write the solution legibly and as detailed as possible for better understanding)
In a M/M/1 model, and the average time a customer waits in the system is 0.75 hour, and the average time a customers waits in the queue is 0.27 hour. Then, the average number of customers in the system is
The poaching model for Species Z is Z' = a Z (1Z) - b where the variable Z represents the population of Species Z and Z = 0.2 when t = 0. If a = 0.4 and b = 0.14, what can be said about the population of Species Z in the long run? a) The population will level off near 85% of its carrying capacity. b) The population will level off near 79% of its carrying capacity. c) The population will die off. od) The population will level off near 66% of its carrying capacity.

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