Epidemics. A model for the spread of contagiousdiseases is obtained by assuming that the rate of spreadis proportional to the number of contacts betweeninfected and noninfected persons, who are assumed tomove freely among each other. Set up the model. Findthe equilibrium solutions and indicate their stability orinstability. Solve the ODE. Find the limit of theproportion of infected persons as 1→x and explainwhat it means.

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Answered: & Epidemics. A model for the spread of…

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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5. Find E (p) for the price-demand equation Find and interpret each of the following: (a) E (8), E (30), (b) (c) z=f(p) 1000 (40-p). E (20).
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View Image : Find the demand function for a clock manufacturer if marginal demand, in dollars, is given by and , where is the number of thousands of clocks sold.
The teenage birthrate in the United States has declined since 1995 as shown to the right. Let B be the American teenage birthrate (number of births per 1000 women ages 15-19) at t years since 1995. a. Find an equation of a linear model to describe the data. b. Predict the teenage birthrate in 2020. Then predict the number of births to women in 2020, assuming that there will be 11,007,000 women ages 15-19 in that year. c. Predict in which years the birthrate will be less than 11.4 births per 1000 women ages 15-19. Birthrate (number of births per 1000 women ages 15-19) Year 1995 56.0 2000 47.7 2005 40.5 2010 34.3 2015 24.2 a. Using the points (0,56.0) and (10,40.5), the equation of linear model is B = (Use integers or decimals for any numbers in the expression.) Enter your answer in the answer box and then click Check Answer.
2. A simple curve that often makes a good model for the variable costs of a company, as a function of the number of units produced, x, has the form: y = b₁x + b₂x² + b3x³. (There is no constant term because fixed costs are not included.) Consider the following table of recorded variable costs versus units produced for some company:
Consider the web model with the supply and demand equations given by Find the intertemporal equilibrium price, and determine the equilibrium rate and its stability.
Marine scientists use a linear model for the speed c of sound in the oceans as a function of the salinity S at a fixed depth and temperature.† In the following table, one scientist recorded data for c and S at a depth of 500 meters and a temperature of 15 degrees Celsius. Here c is measured in meters per second and S in parts per thousand. Salinity S Sound speed c 35.0 1515.36 35.6 1516.08 36.2 1516.80 36.8 1517.62 37.4 1518.24 (a) Looking over the table, the scientist realizes that one of the entries for sound speed is in error. Which entry is it?S = What is the correct speed?c = m/sec(b) Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature. The slope means that, at the given depth and temperature, for an increase in salinity of part per thousand the speed of sound increases by meters per second. (c) Calculate c(38.2).c(38.2) = m/secExplain in practical terms what it means. This means…
For Shock G: Suppose the economy starts in the long run equilibrium. Illustrate changes that the shock will cause in the short run (using AD-SRAS). Explain why each curve shifts. Determine how the price level and output will be affected in the short run. Mark the output gap on the diagram. Is the output gap positive or negative? Is the economy is booming, or is it in a recession? On the same diagram illustrate how the economy will adjust to the shock in the long run and explain the mechanism. Determine how the price level and output will be affected in the long run. G. The government increases its spending on national defense As a result of this shock, in the short run the (SRAS Curve/AD Curve) will shift? In consequence, in the short run prices and output will? In the short run, there will be a ? (negative/postive) output gap,which means there will be a ? (boom/recession) As time passes, because of high unemployment the wages in the economy will? (decrease/increase) As a…

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