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This case study is about fitting data to various exponential-type functions. (Chapter 5) A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer 250 500 750 1000 1250 1500 1750 2000 (pounds/acre) Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is each pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earned per acre from your graph. Call this estimate k. • Compute a linear regression for the data. • Compute a logarithmic regression(LnReg) for the data. • Use trial and error on your calculator to fit a function of the form r = k(1 – b*) where k is the estimate for the maximum amount of revenue and 0 < b <1 • Choose the best model for revenue and then write a total cost function for fertilizer. Use a graph on your calculator to find where cost equals revenue. • Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.

This case study is about fitting data to various exponential-type functions. (Chapter 5) A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer 250 500 750 1000 1250 1500 1750 2000 (pounds/acre) Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is each pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earned per acre from your graph. Call this estimate k. • Compute a linear regression for the data. • Compute a logarithmic regression(LnReg) for the data. • Use trial and error on your calculator to fit a function of the form r = k(1 – b*) where k is the estimate for the maximum amount of revenue and 0 < b <1 • Choose the best model for revenue and then write a total cost function for fertilizer. Use a graph on your calculator to find where cost equals revenue. • Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.1: Logistic Functions
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This case study is about fitting data to various exponential-type functions. (Chapter 5) A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer 250 500 750 1000 1250 1500 1750 2000 (pounds/acre) Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is each pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earned per acre from your graph. Call this estimate k. • Compute a linear regression for the data. • Compute a logarithmic regression(LnReg) for the data. • Use trial and error on your calculator to fit a function of the form r = k(1 – b*) where k is the estimate for the maximum amount of revenue and 0 < b <1 • Choose the best model for revenue and then write a total cost function for fertilizer. Use a graph on your calculator to find where cost equals revenue. • Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.
Transcribed Image Text:This case study is about fitting data to various exponential-type functions. (Chapter 5) A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer 250 500 750 1000 1250 1500 1750 2000 (pounds/acre) Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is each pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earned per acre from your graph. Call this estimate k. • Compute a linear regression for the data. • Compute a logarithmic regression(LnReg) for the data. • Use trial and error on your calculator to fit a function of the form r = k(1 – b*) where k is the estimate for the maximum amount of revenue and 0 < b <1 • Choose the best model for revenue and then write a total cost function for fertilizer. Use a graph on your calculator to find where cost equals revenue. • Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.
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