8 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→0 and explainwhat it means.

The rate of spread of diseases is proportional to the number of contacts between infected and…

Answered: Epidemics. A model for the spread of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Carbon Dioxide Emissions The table gives the millions of metric tons of carbon dioxide emissions frombiomass energy combustion in the United States forselected years from 2010 projected to 2032.a. Find a linear function that gives the millions ofmetric tons of carbon dioxide emissions, y, asfunction of x, the number of years after 2010.b. Graph the model on the same axes with the data.Is it a good fit for the data?c. What does the (unrounded) model predict the millions of metric tons of carbon dioxide emissionswill be in 2027? d. When will the millions of metric tons of carbondioxide emissions reach 776.6, according to themodel?
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…
PopulationThe resident population of Wisconsin (in thousands) was 5655 in 2009 and 5743 in 2013. Assume that the relationship between the population y and the year t is linear. Let t = 0 represent 2000. (Source: U.S. Census Bureau) (a) Write a linear model for the data. What is the slope and what does it tell you about the population? (b) Use the model to estimate the population in 2011. (c) Use your school’s library, the Internet, or some other reference source to find the actual population in 2011. How close was your estimate? (d) Do you think your model could be used to predict the population in 2018? Explain

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