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Problem 1. The following data table shows the probability P, as a percentage, of a college football team converting on fourth down versus the distance D, in yards, to the first down marker. D distance in yards Probability (as a percent) 1 2 3 4 5 6 7 8 70 60 53 46 41 37 34 32 Suppose we use the one parameter exponential model to fit the data f(D) = 100e" D. (a) Why does it make sense to have the 100 in front of the erD in our proposed model? (b) Set up the sum of squared errors (SSE) function that incorporates your model f(D) = 100erD and data in the table. Give the answer in summation notation. (c) Use calculus to find the parameter r that minimizes the SSE function. However, first apply the natural logarithm to both sides of our model. Use summation notation and clearly show all your steps. - Hint: the following logarthmic identity is helpful: In(a b) ln(a) + In(b) (d) Show what needs to be entered into desmos to find the value of the parameter r that minimizes the SSE function. (e) Give your best fit exponential model that you found above.

Problem 1. The following data table shows the probability P, as a percentage, of a college football team converting on fourth down versus the distance D, in yards, to the first down marker. D distance in yards Probability (as a percent) 1 2 3 4 5 6 7 8 70 60 53 46 41 37 34 32 Suppose we use the one parameter exponential model to fit the data f(D) = 100e" D. (a) Why does it make sense to have the 100 in front of the erD in our proposed model? (b) Set up the sum of squared errors (SSE) function that incorporates your model f(D) = 100erD and data in the table. Give the answer in summation notation. (c) Use calculus to find the parameter r that minimizes the SSE function. However, first apply the natural logarithm to both sides of our model. Use summation notation and clearly show all your steps. - Hint: the following logarthmic identity is helpful: In(a b) ln(a) + In(b) (d) Show what needs to be entered into desmos to find the value of the parameter r that minimizes the SSE function. (e) Give your best fit exponential model that you found above.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 70E
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answer problem 1a, 1b, 1c, 1d, and 1e and show work/ explain how you got the answer
Problem 1. The following data table shows the probability P, as a percentage, of a college football team converting on fourth down versus the distance D, in yards, to the first down marker. D distance in yards Probability (as a percent) 1 2 3 4 5 6 7 8 70 60 53 46 41 37 34 32 Suppose we use the one parameter exponential model to fit the data f(D) = 100e" D. (a) Why does it make sense to have the 100 in front of the erD in our proposed model? (b) Set up the sum of squared errors (SSE) function that incorporates your model f(D) = 100erD and data in the table. Give the answer in summation notation. (c) Use calculus to find the parameter r that minimizes the SSE function. However, first apply the natural logarithm to both sides of our model. Use summation notation and clearly show all your steps. - Hint: the following logarthmic identity is helpful: In(a b) ln(a) + In(b) (d) Show what needs to be entered into desmos to find the value of the parameter r that minimizes the SSE function. (e) Give your best fit exponential model that you found above.
Transcribed Image Text:Problem 1. The following data table shows the probability P, as a percentage, of a college football team converting on fourth down versus the distance D, in yards, to the first down marker. D distance in yards Probability (as a percent) 1 2 3 4 5 6 7 8 70 60 53 46 41 37 34 32 Suppose we use the one parameter exponential model to fit the data f(D) = 100e" D. (a) Why does it make sense to have the 100 in front of the erD in our proposed model? (b) Set up the sum of squared errors (SSE) function that incorporates your model f(D) = 100erD and data in the table. Give the answer in summation notation. (c) Use calculus to find the parameter r that minimizes the SSE function. However, first apply the natural logarithm to both sides of our model. Use summation notation and clearly show all your steps. - Hint: the following logarthmic identity is helpful: In(a b) ln(a) + In(b) (d) Show what needs to be entered into desmos to find the value of the parameter r that minimizes the SSE function. (e) Give your best fit exponential model that you found above.
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