la Sociologists model the spread of rumors using logistic equations. The key assumption is that at any given time a fraction y of the population, where 0sys1, knows the rumor, while the remaining fraction 1-y does not. Furthermore, the rumor spreads by interactions between those who know the rumor and those who do not. The number of such interactions is proportional to y(1-y). Therefore, the equation that describes the spread of the rumor is y' (1) = ky(1 - y), where k is a positive real number. The fraction of people who initially know the rumor is y(0) = yo, where 0sy, s 1. Complete parts (a) to (c) below. ....... a. Solve this initial value problem and give the solution in terms of k and yo- Start by writing y'(t) = ky(1- y) in separated form. dy = kdt y(1-y) eBook Integrate both sides. In = kt +C (Do not simplify.) ntents Raise e to the power of each side of the equation. y uccess kt 1-y ia Library Take the recinrocal of each sirde of the enuation

la Sociologists model the spread of rumors using logistic equations. The key assumption is that at any given time a fraction y of the population, where 0sys1, knows the rumor, while the remaining fraction 1-y does not. Furthermore, the rumor spreads by interactions between those who know the rumor and those who do not. The number of such interactions is proportional to y(1-y). Therefore, the equation that describes the spread of the rumor is y' (1) = ky(1 - y), where k is a positive real number. The fraction of people who initially know the rumor is y(0) = yo, where 0sy, s 1. Complete parts (a) to (c) below. ....... a. Solve this initial value problem and give the solution in terms of k and yo- Start by writing y'(t) = ky(1- y) in separated form. dy = kdt y(1-y) eBook Integrate both sides. In = kt +C (Do not simplify.) ntents Raise e to the power of each side of the equation. y uccess kt 1-y ia Library Take the recinrocal of each sirde of the enuation

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...

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What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?
What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?
Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.
Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.
The table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.
What is the y -intercept on the graph of the logistic model given in the previous exercise?
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Eastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?