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Consider the following table. (Note: This exercise corresponds to the subsection Model Choices.) Production, Given the Amount Invested in Capital Capital, x (million dollars) Production, P (billion units) 6 20 18 37 24 41 30 42 59 48 78 (a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior A scatter plot of the data isSelect and appears to have an inflection point near x = 24. The scatter plot is concaveSelect to the left of x 24 and concaveSelect to the right of x 24. This behavior suggests a -Select function. (b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility. OProduction should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. Production should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. OProduction should continue to increase to a limiting value as capital expenditure increases. A logistic model would fit this possibility. Production should approach 0 as capital expenditure increases. A logistic model would fit this possibility. (c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 x S 48. (Round all numerical values to four decimal places.) P(x) (d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 xs 48. (Round all numerical values to four decimal places.) P(x) =

Consider the following table. (Note: This exercise corresponds to the subsection Model Choices.) Production, Given the Amount Invested in Capital Capital, x (million dollars) Production, P (billion units) 6 20 18 37 24 41 30 42 59 48 78 (a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior A scatter plot of the data isSelect and appears to have an inflection point near x = 24. The scatter plot is concaveSelect to the left of x 24 and concaveSelect to the right of x 24. This behavior suggests a -Select function. (b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility. OProduction should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. Production should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. OProduction should continue to increase to a limiting value as capital expenditure increases. A logistic model would fit this possibility. Production should approach 0 as capital expenditure increases. A logistic model would fit this possibility. (c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 x S 48. (Round all numerical values to four decimal places.) P(x) (d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 xs 48. (Round all numerical values to four decimal places.) P(x) =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
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Consider the following table. (Note: This exercise corresponds to the subsection Model Choices.) Production, Given the Amount Invested in Capital Capital, x (million dollars) Production, P (billion units) 6 20 18 37 24 41 30 42 59 48 78 (a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior A scatter plot of the data isSelect and appears to have an inflection point near x = 24. The scatter plot is concaveSelect to the left of x 24 and concaveSelect to the right of x 24. This behavior suggests a -Select function. (b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility. OProduction should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. Production should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. OProduction should continue to increase to a limiting value as capital expenditure increases. A logistic model would fit this possibility. Production should approach 0 as capital expenditure increases. A logistic model would fit this possibility. (c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 x S 48. (Round all numerical values to four decimal places.) P(x) (d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 xs 48. (Round all numerical values to four decimal places.) P(x) =
Transcribed Image Text:Consider the following table. (Note: This exercise corresponds to the subsection Model Choices.) Production, Given the Amount Invested in Capital Capital, x (million dollars) Production, P (billion units) 6 20 18 37 24 41 30 42 59 48 78 (a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior A scatter plot of the data isSelect and appears to have an inflection point near x = 24. The scatter plot is concaveSelect to the left of x 24 and concaveSelect to the right of x 24. This behavior suggests a -Select function. (b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility. OProduction should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. Production should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. OProduction should continue to increase to a limiting value as capital expenditure increases. A logistic model would fit this possibility. Production should approach 0 as capital expenditure increases. A logistic model would fit this possibility. (c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 x S 48. (Round all numerical values to four decimal places.) P(x) (d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 xs 48. (Round all numerical values to four decimal places.) P(x) =
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