Question 821614: 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
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?
Use the table to evaluate and interpret p(0). What is a possible explanation for this?
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.
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.
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?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
company A:
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to calculate the linear equation represented by the data, copy and paste this data:
0 7
500 25.50
1000 44
1500 62.50
2000 81
2500 99.50
3000 118
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into this solver:
https://sooeet.com/math/linear-regression.php
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y-intercept: 7
slope: 0.037
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slope-intercept form of the line that models the given data:
p(x) = 0.037x + 7
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p(x) is perfectly linear
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price per cup = slope = $0.037 = 3.7 cents
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weekly delivery charge = y-intercept = p(0) = $7
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company B:
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the linear model for company B:
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p(x) = 0.039x + 3.5
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the student should do all remaining work
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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