In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product. T = −2n3 + 3n2 + n (a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units. (b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.) T( ) Calculate that value. (Round your answer to two decimal places.) thousand units (c) Find the approximate location of the inflection point. (Round your answers to one decimal place.) (n, T) = ( , ) Explain what it means in practical terms. (d) What is the maximum amount produced? (Round your answer to two decimal places.) T = thousand units
In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product. T = −2n3 + 3n2 + n (a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units. (b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.) T( ) Calculate that value. (Round your answer to two decimal places.) thousand units (c) Find the approximate location of the inflection point. (Round your answers to one decimal place.) (n, T) = ( , ) Explain what it means in practical terms. (d) What is the maximum amount produced? (Round your answer to two decimal places.) T = thousand units
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 43E
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In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product.
T = −2n3 + 3n2 + n
(a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units.
(b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.)
T( )
Calculate that value. (Round your answer to two decimal places.)
thousand units
(c) Find the approximate location of the inflection point. (Round your answers to one decimal place.)
Explain what it means in practical terms.
(d) What is the maximum amount produced? (Round your answer to two decimal places.)
T = thousand units
(b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.)
T( )
Calculate that value. (Round your answer to two decimal places.)
thousand units
(c) Find the approximate location of the inflection point. (Round your answers to one decimal place.)
(n, T) | = | ( , ) |
Explain what it means in practical terms.
(d) What is the maximum amount produced? (Round your answer to two decimal places.)
T = thousand units
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