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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Suppose that t weeks after the start of an epidemic in a certain community, the number P(t) of people who have caught the disease is given by the logistic curve P(t) =3000 5+295e−0.3t (a) How many people had the disease when the epidemic began? (b) Approximately how many people in total will get the disease? (c) When was the disease spreading most rapidly? (d) How fast was the disease spreading at the peak of the epidemic? (e) When did the spread of the disease start to slow down? (f) What is the differential equation for P(t)? g) By the time 400 people had the disease, what was the rate at which the disease was spreading?
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- Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 120% per year. If the starting population is given by po = 500, then after one breeding season the population of the pond is given by P1 = Round your answer to the nearest integer.arrow_forwardIn the early 1980s, AIDS (Acquired Immune Deficiency Syndrome) spread rapidly. A logistic curve modeling the spread of the disease in the United States is given by 47500 P(t) = 1+ 148.41e-0.8t where t is measured in years since 1981 and P is the number of reported cases. In what year does this model predict that the number of new cases will be growing at the largest rate? Remember to fully justify your answer.arrow_forwardThe table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain country. Complete parts (a) and (b) below. (a) Find an exponential model of the form f(t)=yob' for these data, where t=0 corresponds to the year 2000.Use the first and last data points to find a function. 1(t)=¹ (Round to two decimal places as needed.) (b) Assuming the model remains accurate, estimate the death rate in 2019 and 2024. The death rate in 2019 will be (Round to one decimal place as needed.) people per 100,000 The death rate in 2024 will be (Round to one decimal place as needed.) people per 100,000. Year 2000 2002 2004 2006 2008 2010 2012 2014 Death Rate 257.4 239.4 215.0 211.9 185.6 178.9 171.8 166.0arrow_forward
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