Lesson 12: Avi & Benita s Repair Shop
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- Mercy Tucker
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1 : Avi & Benita s Repair Shop Opening Exercise Avi and Benita run a repair shop. They need some help, so they hire you. Avi and Benita have different options for how much they'll pay you each day. In this Desmos activity, you ll explore those options. Let s get started! You will need: the class code for Avi & Benita s Repair Shop, Chromebook 1. Use the class code given to you by your teacher and begin the Avi & Benita s Repair Shop activity on Desmos. Once you are finished with the Desmos activity, discuss the following questions in your group.. Did your opinion of each option change as you completed the activity? 3. On Screen 8, a new employee starts working at Avi and Benita s repair shop. What advice did you give the new employee? Why? 4. On Screen 9, you are asked to decide which option is best if you are NOT allowed to change once you choose an option. Which option do you think is best? Explain your thinking. : Avi & Benita s Repair Shop Unit 6: Exponential Functions & Their Applications S.139
2 Hart Interactive Algebra 1 5. On Screens 3 and 6, you are asked to complete a table of values for each option. Use the table below to recreate those values. Then graph them on the grid provided. Be sure to include a legend. Day Avi s Rule in dollars Benita s Rule in dollars : Unit 6: Avi & Benita s Repair Shop Exponential Functions & Their Applications S.140
3 6. A. Estimate the day Avi s option become a better choice than Benita s. How can you tell? B. Estimate the day Benita s option become a better choice than Avi s. How can you tell? Although the data is discrete, we ll connect the points so that we can write equations for each function as if they were continuous. 7. Discuss with your partner the difference between discrete and continuous data. 8. A. Benita s option is a linear function. What is the slope of this function? B. What is the y-intercept of this function? C. What is the equation for Benita s data? 9. Avi s option is a non-linear function. A. What type of function could model Avi s data? d B. The explicit formula f( d) = a b can be used to model Avi s data. In this case, a represents the initial amount, b represents the growth factor and d represents the day. Use the data in the table to write the equation for Avi s data. : Avi & Benita s Repair Shop Unit 6: Exponential Functions & Their Applications S.141
4 Lesson Summary The Venn diagram below compares linear and nonlinear functions. Linear Functions Nonlinear Functions y = mx + b A line is formed when it is graphed. Any equation as long as it isn t of the form y = mx + b The graph is a curve, set of segments or rays, or a combination of both, or a set of discrete data points. All of these can be graphed. All must pass the Vertical Line Test. These can also be of the form y = number. : Avi & Benita s Repair Shop Unit 6: Exponential Functions & Their Applications S.14
5 Homework Problem Set Determine if the table in each problem can represent a linear function. Explain your thinking x y x y x y Determine if the graph in each problem is representing a linear or a nonlinear function Determine if the equation in each problem is representing a linear or a nonlinear function. 7. fx () = x 1 8. fx () = x 1 9. fx () = 3+ 4x : Avi & Benita s Repair Shop Unit 6: Exponential Functions & Their Applications S.143
6 Choose the Best Option Two equipment rental companies have different penalty policies for returning a piece of equipment late. Company 1: On day 1, the penalty is $5. On day, the penalty is $10. On day 3, the penalty is $15. On day 4, the penalty is $0, and so on, increasing by $5 each day the equipment is late. Company : On day 1, the penalty is $0.01. On day, the penalty is $0.0. On day 3, the penalty is $0.04. On day 4, the penalty is $0.08, and so on, doubling in amount each additional day late. Jim rented a digger from Company because he thought it had the better late return policy. The job he was doing with the digger took longer than he expected, but it did not concern him because the late penalty seemed so reasonable. When he returned the digger 15 days late, he was shocked by the penalty fee. 10. Why is Company a more expensive option for Jim? 11. Use the table below to see the charges over the 15 late days. Company 1 Company Day Penalty Day Penalty : Avi & Benita s Repair Shop Unit 6: Exponential Functions & Their Applications S.144
7 1. Which company has a greater 15-day late charge? 13. Describe how the amount of the late charge changes from any given day to the next successive day in both Companies 1 and. 14. A. Write a formula for the sequence that models the data in the table for Company 1. B. Is the sequence arithmetic, geometric, or neither? Is the formula linear, exponential or neither? 15. A. Write a formula for the sequence that models the data in the table for Company. B. Is the sequence arithmetic, geometric, or neither? Is the formula linear, exponential or neither? 16. How much would the late charge have been after 0 days under Company 1? Company? 17. Which of the two penalties grows more quickly? Why? : Avi & Benita s Repair Shop Unit 6: Exponential Functions & Their Applications S.145
8 18. Sketch a graph of a linear function. 19. Sketch a graph of a nonlinear function. Spiral Review Evaluating functions Determine the value of f() and f(-) for each equation below. 0. fx () = x 1 1. fx () = x 1. fx () = 3+ 4x 3. fx () = x 1 4. fx () = x 1 5. fx () = 3+ 4x 6. fx () = x 1 7. fx () = x 1 8. fx () = 3+ 4x : Avi & Benita s Repair Shop Unit 6: Exponential Functions & Their Applications S.146
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