Part A As the company has increased in popularity, it has continued to add employees in all departments. The production facility manager has provided data that shows the relationship between the number of units produced in an hour and the number of workers on the production line during that hour. The data is shown in the table.

Number of Workers 17 19 21 23 25 27 29 31
Units Produced 842 892 943 992 1,040 1,092 1,142 1,192
Question 1
What type of function would best model the data? Use observations of the output values to justify your answer.

Question 2
Use the graphing tool to plot the data. Does the scatter plot verify your choice of function model? Explain why or why not.

Question 3
Use the graphing tool and the best fit function of the tool to write a function that models the data. Round coefficients and constants to the nearest hundredth, if necessary.

Question 4
Faster Fidget predicts that the current demand for its product is going to require the production line to produce about 2,300 fidget spinners every hour. How many workers should Marco recommend that the production facility keep on the line to meet this goal? Show your work.

Part B
Faster Fidget unveiled a light-up fidget spinner three months ago. Its sales team has been monitoring the daily unit sales of this specific model of fidget spinner to determine whether to continue its production. The company has provided Marco with approximate daily unit sales (rounded to the nearest hundred) after a specific number of days on the market. The data is shown in the table.

Days on Market 20 30 40 50 60 70 80 90
Units Sold Daily 1,800 6,200 11,100 13,900 15,200 14,400 10,500 6,700
Question 1
Use the graphing tool to plot the data. Use the Insert Image button to insert a screenshot of your graph in the answer space.

Question 2
What type of function would best model the data? Explain your reasoning.

Question 3
Use the graphing tool and the best fit function of the tool to write a function that models the data. Round coefficients and constants to the nearest hundredth, if necessary.

Question 4
The sales team has noticed that the daily unit sales are decreasing and has decided to stop production of the light-up spinner once daily unit sales fall to 1,500 or below. A company founder has asked Marco if he thinks the light-up spinner will continue to be in production after 100 days on the market. What should Marco’s response be? Show the mathematical justification for your answer.

Part C
The production facility manager is researching the purchase of a new machine that inserts the bearing into the circular center pad of the fidget spinners. Faster Fidget has purchasing guidelines in place that require all equipment to be retired and resold after three years of use. The purchasing guidelines also state that this type of machine can be purchased only if it has a resale value of at least $2,500 at the end of the three years.

As part of her research, the production facility manager has found eight different facilities that have resold the same model of machine. She recorded the machines’ ages, in years, and the corresponding resale value in this table.

Age (years) 0.5 1.5 1.25 2.5 2.25 0.75 2.75 1.0
Resale Value (dollars) 9,800 5,200 6,260 3,570 3,890 8,400 3,390 7,100
The production facility manager has asked Marco to help her use the data to determine whether the purchase of this machine will fall within the company’s purchasing guidelines.

Question 1
Use the graphing tool to plot the data. Use the Insert Image button to insert a screenshot of your scatter plot in the answer space.

Question 2
What type of function would best model the data? Explain your reasoning.

Question 3
Use the graphing tool and the best fit function of the tool to write a function that models the data. Round coefficients and constants to the nearest hundredth, if necessary.

Question 4
Based on the model, should Marco advise the production facility manager that purchasing the new machine is consistent with Faster Fidget’s purchasing guidelines? Show the mathematical justification for your answer.

Part D
In the past month, Faster Fidget unveiled a mini fidget spinner that is quickly becoming its most popular product. The approximate daily sales (rounded to the nearest hundred) after a specific number of days on the market are shown in the table.

Days on Market 3 7 12 17 21 27
Units Sold Daily 321 548 1,030 1,528 2,399 4,123
The sales team decided to perform its own data analysis (without Marco’s help) and used a linear model to predict that the sales will be approximately 4,311 units after 32 days on the market. Is the sales team’s prediction valid? Why or why not? If not, what is a valid prediction?