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A dairy company's records reveal that it costs approximately Cw) = 3750.22 + 78.95 In w dollars for the company to produce w thousand gallons of whole milk each week. The company has been increasing production regularly since opening a new production plant five years ago and plans to continue the same trend of increases over the next ten years. The table shows actual and projected production of whole milk given the number of years since production began at the new plant. Weekly Production of Whole Milk Production (thousand gallons) Year 5.8 7.4 7. 12.2 10 20.2 13 31.4 (0) Find the function for the quadratic model that gives producton of whole milk in thousand gallons each week, where tia the number of years since production began at the new plant, with data from ists 13. (Round all numencal values to three decimal places thousand gallons (b) Use the company's cost model along with the production model to wnte an expression modeling weekly cost as a function of bime. (Round all numerical values to three decimal places.) dollars

A dairy company's records reveal that it costs approximately Cw) = 3750.22 + 78.95 In w dollars for the company to produce w thousand gallons of whole milk each week. The company has been increasing production regularly since opening a new production plant five years ago and plans to continue the same trend of increases over the next ten years. The table shows actual and projected production of whole milk given the number of years since production began at the new plant. Weekly Production of Whole Milk Production (thousand gallons) Year 5.8 7.4 7. 12.2 10 20.2 13 31.4 (0) Find the function for the quadratic model that gives producton of whole milk in thousand gallons each week, where tia the number of years since production began at the new plant, with data from ists 13. (Round all numencal values to three decimal places thousand gallons (b) Use the company's cost model along with the production model to wnte an expression modeling weekly cost as a function of bime. (Round all numerical values to three decimal places.) dollars

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.10: Modeling Variation
Problem 48E
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A dairy company's records reveal that it costs approximately Cw) = 3750 22+ 78.95 In w dollars for the company to produce w thousand gallons of whole milk each week. The company has been increasing production regularly since opening a new production plant five years ago and plans to continue the same trend of increases over the next ten years. The table shows actual and projected production of whole milk given the number of years since production began at the new plant. Weekly Production of Whole Milk Production (thousand gallons) Year 5.0 7.4 7. 12.2 10 20.2 13 31.4 (6) Find the function for the quadratic model that gives production of whole milk in thousand gallons each week, where tia the number of years since production began at the new plant, with data from ists13. (Round all numencal values to three decimal places) w(t) thousand gallons (b) Use the company's cost model along with the production model to wnte an expression modeling weekly cost as a function of time. (Round all numerical values to three decimal places.) dolars
Transcribed Image Text:A dairy company's records reveal that it costs approximately Cw) = 3750 22+ 78.95 In w dollars for the company to produce w thousand gallons of whole milk each week. The company has been increasing production regularly since opening a new production plant five years ago and plans to continue the same trend of increases over the next ten years. The table shows actual and projected production of whole milk given the number of years since production began at the new plant. Weekly Production of Whole Milk Production (thousand gallons) Year 5.0 7.4 7. 12.2 10 20.2 13 31.4 (6) Find the function for the quadratic model that gives production of whole milk in thousand gallons each week, where tia the number of years since production began at the new plant, with data from ists13. (Round all numencal values to three decimal places) w(t) thousand gallons (b) Use the company's cost model along with the production model to wnte an expression modeling weekly cost as a function of time. (Round all numerical values to three decimal places.) dolars
(c) Write the rate-of-change function of the cost function found in part (b). (Round all numerical values to three decimal places.) dollars per year dt (d) Estimate the company's weekly costs 2 and 10 years from now. (Round your answers to two decimal places.) 2 years from now 10 years from now Estimate the rates of change for those same years. (Round your answer to two decimal places.) 2 years from now per year 10 years from now per year
Transcribed Image Text:(c) Write the rate-of-change function of the cost function found in part (b). (Round all numerical values to three decimal places.) dollars per year dt (d) Estimate the company's weekly costs 2 and 10 years from now. (Round your answers to two decimal places.) 2 years from now 10 years from now Estimate the rates of change for those same years. (Round your answer to two decimal places.) 2 years from now per year 10 years from now per year
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