Question

One more big problem!

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.
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.
---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

Ok so,
A- p(x)=(0.037)x+(7.00) ---- the cost per cup is $0.037, the function is linear --- the average rate change is (0.037)
Am I right?

Answer 3

So you determined that the initial delivery charge is the $7.
And that the 500 cups added $18.50 more.

So that works out to 3.7 cents per cup?
Mmm yah looks good so far!

Answer 4

what grade of work is this high school

Answer 5

So (A) is right?

Answer 6

Then (B)- Its will cost $7 just to ship it.
Yes or no?

Answer 7

Your linear function looks good.
For part A they wanted average rate of change.

You `could` apply slope formula to find the slope between 1000 cups and 0 cups.. and do all that business.

But since it's linear, it will have the same slope for the entire function.
So ya A looks good :)

Answer 8

A or E make sense but what do u think

Answer 9

B, yes good good.

Answer 10

Oh oh actually, see at the end of part A?

Answer 11

`What is a possible explanation for this?`
It sounds like they want you to determine that it's linear... by using the slope formula thing.

Answer 12

What do you mean ' at the end of par A?'

Answer 13

This one they didn't `tell us` that the model is linear like the last problem.
Or did they? Maybe I'm just not seeing it in there.

Do you submit this online or something?
Or do you need to show all of your work?
If so, we'll need to find the slope for the first 1000 cups and come up with the slope that way.

Answer 14

y-intercept: 7
slope: 0.037

Answer 15

I have to show my work >.>

Answer 16

p(x) = 0.037x + 7

Answer 17

Right? or no

Answer 18

So to find the slope they wanted us to use these two points (0,7) and (1000,44).

Your function looks good :)
But they wanted you to come up with the slope using particular points.
You're supposed to calculate it using two different sets of points.
And then realize `oh this function is linear, the price of the cups doesn't change or anything because the slope stays the same`.

Answer 19

\[\Large\rm m=\frac{44-7}{1000-0}=0.037\]This is what you determined.
Just make sure you use these particular points.
This is the average for the first 1000 cups.

Answer 20

Like They pay $18.5 for every 500 cups plus a $7 weekly delivery charge.
The graph would be a straight line beginning at (0,7) and going through all the given points to (3000,118)

Answer 21

The average for all cups would be,\[\Large\rm m=\frac{118-7}{3000-0}=0.037\]

Answer 22

But with the order of 3000 cups

Answer 23

You used the 18.5 and 500 cups... they simply wanted you to use the 1000 cups and 44 to come to the same conclusion.

It's fine!! Let's skip part A then lol.

Answer 24

Ok, haha

Answer 25

Understand how to graph this function? :o

Answer 26

The important thing is that you don't make a 1 to 1 graphing.