Question

this is a pretty big question ( its algebra one ) but i really need help with it :)

Answer 1

A coffee shop pays Coffee Delivery Company A, a certain price for each disposable cup it orders plus a weekly delivery charge to remain on the driver’s delivery route. The cups are purchased in increments of 500. To quickly determine how much the coffee shop will be spending on cups before their arrival, the owner created the following table:

Cups Ordered Price
0 $7
500 $25.50
1,000 $44
1,500 $62.50
2,000 $81
2,500 $99.50
3,000 $118

A. The price of the cups, p(x), is a function of the number of x cups ordered. Using the table, determine the average rate of change for the first 1,000 cups ordered and then for all 3,000 cups ordered. What does this tell you about the function?

B. Use the table to evaluate and interpret p(0). What is a possible explanation for this?

C. Sketch a graph, labeling its key features, to show the price the coffee shop would pay Coffee Delivery A to have between 0 and 3,000 cups delivered each week.

D. Create a model using function notation that represents how the two quantities, cups and cost, are related.

The coffee shop found another delivery company that sells orders at increments of 500 cups, Coffee Delivery B. They charge $3.50 each week to be on their delivery route and charge 3.9 cents per disposable cup.

- Make a function using the information about the second delivery company.
- Graph the price the coffee shop would pay for Coffee Delivery B to deliver the same amount of cups on the same graph from Part C, using a different color for the new line.
- If the coffee shop can change delivery companies every three months, when should they consider Coffee Delivery A, and when should they consider Coffee Delivery B?

Answer 2

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