Assume that the population of a city satisfies the logistic hypothesis: "The rate of change of population at any time is proportional to the product of the population at that time and the difference between capacity and population." We have the following data: capacity is 11,825,000, population in 1960 was 3,750,500, and population in 2000 was 4,215,500. (a) Set up and solve an Initial Value Problem to express the population of the city as a function of time. (b) Draw a graph of the population. (c) Calculate an estimate of the population in the year 2030.
Assume that the population of a city satisfies the logistic hypothesis: "The rate of change of population at any time is proportional to the product of the population at that time and the difference between capacity and population." We have the following data: capacity is 11,825,000, population in 1960 was 3,750,500, and population in 2000 was 4,215,500. (a) Set up and solve an Initial Value Problem to express the population of the city as a function of time. (b) Draw a graph of the population. (c) Calculate an estimate of the population in the year 2030.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 44E: Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program...
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Assume that the population of a city satisfies the logistic hypothesis:
"The rate of change of population at any time is proportional to the product of the population at that time and the difference between capacity and population."
We have the following data: capacity is 11,825,000, population in 1960 was 3,750,500, and population in 2000 was 4,215,500.
(a) Set up and solve an Initial Value Problem to express the population of the city as a function of time.
(b) Draw a graph of the population.
(c) Calculate an estimate of the population in the year 2030.
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