3. 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

Question

3.	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

anonymous · Answer

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

anonymous · Answer

@IMStuck help???

anonymous · Answer

just these last 2 i don't understand how to do

anonymous · Answer

can you help?

imstuck · Answer

Ok, I found the function.  I did it by making a graph of the numbers you gave me.  Since the number of cups at 0 starts at $7, that is where the line (linear function) starts.  I graphed the first point (500, 25.5) and then the second point (1000, 44) and then found the slope of the line.  It is .037.  Using the point-slope formula, I got the function f(x) = .037x + 7.  And it works.  For any number of cups (In increments of 500, that is), you will find the price for that amount of cups is what is given on the manager's chart for pricing.  What is the question for E?  Which is the better company to get delivery from?

anonymous · Answer

E.	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.
•	Using a different color to add to the graph sketched in Part C, graph the price the coffee shop would pay for Coffee Delivery B to deliver the same amount of cups.
•	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?
@IMStuck here it is sorry

imstuck · Answer

Ok, I'm back.  I did the same thing with this as I did for the first one: I plotted several points after figuring out that 500 cups at 3.9 cents per cup costs $19.50, and 1000 cups at 3.9 cents per cup costs $39.  I found the slope (.039) and filled in my point-slope equation with that slope and either point.  The formula for the Delivery Co. B is
y = .039x where x is the number of cups in increments of 500, of course.  You should be able to graph this on your own on graph paper because doing it here with the draw tool would not work out well.  If there are any other issues with this please ask!