Polynomials
POLYNOMIAL FUNCTIONS ACTIVITY
NCTM Addenda Series/Grades 9-12
The Park and Planning Commission decided to consider three factors when attempting to improve the daily profits at their sports facility:
❖ The number of all-day admission tickets sold
❖ The cost of operating the facility
❖ The price of each all-day admission ticket
After carefully analyzing their operating costs, they found that it would be impossible to cut them further.
Daily Operating Costs
Advertisements $ 55.00
Employees’ pay 310.00
Heat, lights, taxes, food, rent 435.00
Knowing that the maximum number of potential patrons is 200, the Park and Planning Commission decided to vary the price of each admission ticket to see what effect this change might have on the number of tickets sold. After much experimentation, they collected the following sales data:
Ticket Price [in $] Average Number of Tickets Sold
________________________________________________________________________
5. 158
7 142
9. 119
11 97
1. Using this information, suggest the optimal ticket price for all-day admission to the sports facility. If you feel the need for more information, please explain why.
2. Use a graphing calculator to find the function rule of best fit for the [price, sales] data. Express the number of tickets sold as a function N of the ticket price. That is, N[x} = ?, where x is the price of the ticket. Produce a rough sketch of the [price, sales] data and the fitted function. Do you expect the function to behave like any of the linear, exponential, or rational functions studied so far? If yes, explain your reasoning.
The Park and Planning Commission used an expanded set of [price, sales] data and two basic economic
NCTM Addenda Series/Grades 9-12
The Park and Planning Commission decided to consider three factors when attempting to improve the daily profits at their sports facility:
❖ The number of all-day admission tickets sold
❖ The cost of operating the facility
❖ The price of each all-day admission ticket
After carefully analyzing their operating costs, they found that it would be impossible to cut them further.
Daily Operating Costs
Advertisements $ 55.00
Employees’ pay 310.00
Heat, lights, taxes, food, rent 435.00
Knowing that the maximum number of potential patrons is 200, the Park and Planning Commission decided to vary the price of each admission ticket to see what effect this change might have on the number of tickets sold. After much experimentation, they collected the following sales data:
Ticket Price [in $] Average Number of Tickets Sold
________________________________________________________________________
5. 158
7 142
9. 119
11 97
1. Using this information, suggest the optimal ticket price for all-day admission to the sports facility. If you feel the need for more information, please explain why.
2. Use a graphing calculator to find the function rule of best fit for the [price, sales] data. Express the number of tickets sold as a function N of the ticket price. That is, N[x} = ?, where x is the price of the ticket. Produce a rough sketch of the [price, sales] data and the fitted function. Do you expect the function to behave like any of the linear, exponential, or rational functions studied so far? If yes, explain your reasoning.
The Park and Planning Commission used an expanded set of [price, sales] data and two basic economic