Question

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:

Answer 1

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

@CoconutJJ will give medal I'm desperate for help

Answer 3

@wio

Answer 4

@ganeshie8

Answer 5

What are you confused on?

Answer 6

everything tbh

Answer 7

Lets try A first

Answer 8

How do you calculate Avg Rate of Change

Answer 9

@dtan5457

Answer 10

@fatZak

Answer 11

@DanJS last thing :D then my linear lessons are over :D

Answer 12

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?

Answer 13

Average rate of change is = slope of secant line connecting the 2 points

\[ave~change~=\frac{ p(1000) - p(0) }{ 1000 - 0 } = \frac{ $44 - $7 }{ 1000 } = \frac{ $37 }{ 1000 }\]

Answer 14

change to decimal if you want

Answer 15

Average for 3000 cups ordered --- (3000,118) and (0 , 7) are the 2 points to use for the secant line. The slope of the secant is...
\[ave~change~=\frac{ 118 - 7 }{ 3000 } = \frac{ 111 }{ 3000 }\]

Answer 16

p(x) is the price for x cups ordered, p(0), means he orders zero cups, and p(0)=$7, he is charged 7 dollars for ordering zero cups. That must be the charge for shipping, extra costs

Answer 17

this is all for A?

Answer 18

@DanJS

Answer 19

That was A and B

Answer 20

All of these long story probs are exactly the same, just a different story. A graph of a line.

Answer 21

Yes ur right if u write c and d can u write the letter before the explanation

Answer 22

which is B? @DanJS

Answer 23

is this b p(x) is the price for x cups ordered, p(0), means he orders zero cups, and p(0)=$7, he is charged 7 dollars for ordering zero cups. That must be the charge for shipping, extra costs

Answer 24

B) interpret p(0).

p(0), means he orders zero cups, and p(0)=$7, he is charged 7 dollars for ordering zero cups. That must be the charge for shipping, extra costs

Answer 25

C) to sketch the graph, label the x axis cups ordered, and the Y axis, dollar paid

plot each of those points ( cups, dollars paid)

Answer 26

The slope of the line in the graph will be 18.5 dollars per 500 cups

Answer 27

can u make the graph with desmos like i said last night i dont have graph paper or anything and dont know how to put it in to get the graph

Answer 28

D) 18.5 dollars / 500 cups = 0.037 dollars / 1cup, that is the slope

p(x) = slope*(x) + y intercept

p(x) = 0.037*x + 7

Answer 29

Just go to desmos, and type in
y = 0.037*x+7

make the x axis from 0 to 3000
y axis from 0 to like 150 dollars

Answer 30

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.
c(x) = cost of purchasing x cups @ $0.039 per cup, and 3.50 fee

c(x) = 0.039*x + 3.50

Answer 31

add
y = 0.039x + 3.5
to the graph of the first part

Answer 32

add that to the graphing calculator?

Answer 33

how do i make the x and y axis with #'s in desmos?

Answer 34

its still not working for me @DanJS

Answer 35

Blue Line is First Part, Has Y Intercept of 7 Dollars for Zero Cups
Red Line is Second Part, Has Y intercept of 3.50 dollars for zero cups.

Answer 36

Hit the wrench button in the top right to change the axis ranges

Answer 37

X axis - # Cups
Y axis - Cost

Answer 38

:D thankssss

Answer 39

not sure if it is a question, but the point in the middle where they cross, is where they both will be the same price.

For 1750 cups , they both will cost 71.75

Answer 40

For the very last thing, not sure

-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 41

3 months , would be i guess, 12 weeks

Answer 42

For the first company, 12 weeks would cost a fee of 12*$7 = 84 dollars
second company 12 weeks would cost fee 12 * 3.5 = 42 dollars

Answer 43

but the first company costs less per cup bought, 37 cents vs the second company 39 cents per cup

Answer 44

that's all i got

Answer 45

lol you have by far the longest probs on here

Answer 46

xD yayy thanks so much :D

Answer 47

oh oh oh and the graph for C is that the same one in Blue Line is First Part, Has Y Intercept of 7 Dollars for Zero Cups
Red Line is Second Part, Has Y intercept of 3.50 dollars for zero cups.

Answer 48

yeah

Answer 49

:D thankssss :D ur the best really and I'm going to write a testimonial for u :D

Answer 50

haha, thanks :), no more 20 page probs please!

Answer 51

nah its cool

Answer 52

xD hhhhhh ok i promise well i cant keep that promise XD but i'll give u a page at a time xD

Answer 53

Just the all are the same, just different story to go with them. Equations for a line.