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: 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,

Answer 1

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:
http://www.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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Answer 2

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:
www.sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
http://www.sooeet.com/math/quadratic-formula-solver.php
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solve systems of linear equations up to 4-equations 4-variables:
http://www.sooeet.com/math/system-of-linear-equations-solver.php