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Get Full Access to A First Course In Differential Equations With Modeling Applications - 10 Edition - Chapter 3.2 - Problem 23e
Get Full Access to A First Course In Differential Equations With Modeling Applications - 10 Edition - Chapter 3.2 - Problem 23e

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# plots (or scatter diagrams) and least squares linear fit.

ISBN: 9781111827052 44

## Solution for problem 23E Chapter 3.2

A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 23E

Regression Line Read the documentation for your CAS on scatter plots (or scatter diagrams) and least squares linear fit. The straight line that best fits a set of data points is called a regression line or a least squares line. Your task is to construct a logistic model for the population of the United States, defining f (P) in (2) as an equation of a regression line based on the population data in the table in 4. One way of doing this is to approximate the left-hand side of the first equation in (2), using the forward difference quotient in place of dP/dt: (a) Make a table of the values t, P(t), and Q(t) using t=0, 10, 20, . . . , 160 and h = 10. For example, the first line of the table should contain t = 0, P(0), and Q(0). With P(0) = 3.929 and P(10) = 5.308, Note that Q(160) depends on the 1960 census population P(170). Look up this value.(b) Use a CAS to obtain a scatter plot of the data (P(t), Q(t)) computed in part (a). Also use a CAS to find an equation of the regression line and to superimpose its graph on the scatter plot.(c) Construct a logistic model dP/dt = Pf (P), where f (P) is the equation of the regression line found in part (b).(d) Solve the model in part (c) using the initial condition P(0) = 3.929.(e) Use a CAS to obtain another scatter plot, this time of the ordered pairs (t, P(t)) from your table in part (a). Use your CAS to superimpose the graph of the solution in part (d) on the scatter plot.(f) Look up the U.S. census data for 1970, 1980, and 1990. What population does the logistic model in part (c) predict for these years? What does the model predict for the U.S. population P(t) as

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Week 2 – Econ 2106 Key Chapter 2: Model Building and Gains From Trade Chapter 3: The Market at Work – Supply and Demand Terms 1. Absolute Advantage: the ability of one producer to make more than another producer with the same quantity of resources. 2. Capital Goods: goods that help produce other valuable goods 3. Ceteris Paribus: the concept under which economists examine a change in one variable within holding everything else constant 4. Consumer Goods: goods meant for current consumption 5. Endogenous Factors: the variables that can be controlled in a model 6. Exogenous Factors: the variables that cannot be controlled for in a model 7. Investment: using resources to produce new capital 8. Law of Increasing Relative Cost: law stating that the opportunity cost of pro

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