Supposed a student carrying a COVID-19 virus returns to an isolatedcollege campus of 1000 students. Determine a differential equation forthe number of people x(t) who have contracted the virus if the rate atwhich the disease spreads is proportional to the number of interactionsbetween the number of students who have the virus and the number ofstudents who have not yet been exposed to it.

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Answered: Supposed a student carrying a COVID-19…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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mRNA is an intermediate molecule that arises in the decoding of DNA. mRNA is produced by a process called transcription and it eventually decays. Suppose that the rate of transcription is changing exponentially according to the expression ebt and mRNA has a constant per capita decay rate of k. The number of mRNA transcript molecules, T, thus changes as dT dt = ebt - KT. The first term on the right side is time-varying. As a result, the differential equation is not separable. However, the equation can be solved using the change of variables y(t) = bektT(t). Solve the differential equation using this technique. (Let T(0) = To.) T(t) =
Find a linear differential equation with constant coefficients whose general solution is
A forest is inhabited by rabbits and foxes. Every year, each rabbit gives birth to 7 babies and each fox gives birth to 2 babies on average. Foxes try to catch and eat rabbits; each month, each fox has a 3% chance of catching each of the rabbits present in the forest. Each month, every fox that does not eat a rabbit starves to death. Write the differential equations for the number of foxes and rabbits in the forest.
Describe the separation-of-variables technique for obtainingthe solution to a differential equation.
Log(Wagei) = α + β1Educationi + β2Femalei + β3Non Whitei + β4Educationi × Femalei + εi For males, and holding other variables constant, the regression output from the linear regression model above implies that an extra year of education is associated with what percent change in wages?
The rate of increase of COVID-19 infection is directly proportional to the number of people infected and to the number people not yet infected. An isolated remote barangay of population 10,000 records its first case on June 15, 2020. After two days, 100 people are infected. Develop a model that predicts the number of COVID-19 cases in the barangay. How long will it take for 90% of the population to be infected? Assume that the virus persists in the person infected.
Differential equations have been used extensively in the study of drug dissolution for patients given oral medications. The three simplest equations used are the zero-order kinetic equation, the Noyes-Whitney equation, and the Weibull equation. All assume that the initial concentration is zero but make different assumptions about how the concentration increases over time during the dissolution of the medication. The zero-order kinetic equation states that the rate of change in the concentration of drug c (in mg/mL) during dissolution is governed by the differential equation dc dt = k where k is a positive constant. Is this differential equation pure-time, autonomous, or nonautonomous? pure time autonomous nonautonomous State in words what this differential equation says about how drug dissolution occurs. The drug concentration increases linearly with time during dissolution. The drug concentration remains constant with time during dissolution. The drug concentration…
Prove that the linearity of this differential equation is non-linear. Explain the cause of it's linearity.
Disease epidemics can be modelled by differential equations. Suppose we have two sub-populations of individuals in a city: individuals who are infected with some virus (I) and individuals who are susceptible to infection (S). We assume that if a susceptible person interacts with an infected person, there is a probability p that the susceptible person will become infected. Each infected person recovers from the infection at a rate r and becomes susceptible again. The differential equations that model these population sizes are TI - PSI, dS dt dI dt pSI - TI. (a) Assuming no one dies from the virus, the total population N is a constant number defined as N = S+I. Show in this case that you can reduce the above system to the single differential equation for I. (b) Find the general solution I(t) to the ODE found in part (a). (c) If I (0) = Io, give the equation for the unknown constant in terms of Io, N, p and r.
For the two armies X and Y, the X army is about to attack Y army which has only 7725 troops while the X army has 12440 troops. The Y army however superior military equipment’s which make each Y soldier 1.5 times as effective as X soldier. Develop a mathematical model using differential equations and explain for i) which army will win ii) Estimate how many troops of the winning army will be left at the end. iii) How long the battle will end. The kill rates of X and Y are 0.5 and 0.75 respectively.

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