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?

Answer 2

Look at the table, can you find the average rate of change between x=0 and x = 1000 ?

Answer 3

Umm.... $37

Answer 4

how ? whats the formula for average rate of change ?

Answer 5

"average rate of cahnge" is just a fancy name for the most familiar term "slope"

Answer 6

(0, 7)
(1000, 44)

can you find the slope ?

Answer 7

OHH it's slope?! somebody told me it was something else oh my god!

Answer 8

yes, so whats the average rate of change(slope) between x=0 and x=1000 ?

Answer 9

37/1000

Answer 10

Yes ! next find the slope between x=0 and x=3000

Answer 11

look at the table y values again

Answer 12

37/1000

Answer 13

yes ! so what can we conclude ?

Answer 14

the average rate of change(slope) in both intervals is same
so that means the funciton may be a line ?

Answer 15

so the charge for each cup would be something like 0.037?

Answer 16

exactly !

Answer 17

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.

Answer 18

@ganeshie8

Answer 19

is the graph correct?

Answer 20

looks good !

Answer 21

you may even draw a straight line through those two points...

Answer 22

Okay, thanks! :)

Answer 23

yw :)

Answer 24

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

Answer 25

pick a point : (0, 7)
slope = 0.037

write the equation of line ?

Answer 26

\[\large y - 7 = 0.037(x-0)\]

Answer 27

\[\large y = 0.037x + 7\]

Answer 28

or maybe this looks better :

\[\large P(c) = 0.037c + 7\]

Answer 29

this is what i got..

Answer 30

function notation ^^

Answer 31

is it correct?

Answer 32

im getting below graph :

Answer 33

are u graphing : `y = 0.037x + 7` ?

Answer 34

make sure you're not entering too many zeroes after decimal

Answer 35

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.

Answer 36

@ganeshie8

Answer 37

3.5 is the fixed charge (y intercept)
3.9 cents = 0.039 (slope)

create a function ?

Answer 38

y = 0.039x + 3.5 ?

Answer 39

does that look good ?

Answer 40

ohh lol sorry the question just didnt make sense to me, i have two more!

•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

so which company do u think is costly ?

Answer 42

0.037 per cup is costly

or

0.039 per cup is costly

??

Answer 43

B sorry computer froze

Answer 44

careful, B company has lower weekly charge compared to A company

Answer 45

A

Answer 46

i know which one is more costly, i thought A until u said

0.037 or 0.039 so i went with 0.039 sorry

Answer 47

that means B company looks better in the start, but A company is best in the long run

Answer 48

Notice that B company stays low in the beginning,
but after some weeks, it overtakes A and becomes costlier than A

Answer 49

B company starts low, but overtakes precicely when `x = 1750`, and after that stays costlier than A company.

So B company is only good for upto 1750 cups, after that it is better to switch to A company.

Answer 50

if that makes any sense...

Answer 51

Yes it does, thanks!