Data Plan Cost The monthly cost C, in dollars, for wireless data plans with x gigabytes of data included is shown in the table below. Since each input value for x corresponds to exactly one output value for C, the plan cost is a function of the number of data gigabytes. Thus C(x) represents the monthly cost for a wireless data plan with x gigabytes included.
GB | Cost ($) | GB | Cost ($) |
4 | 70 | 20 | 150 |
6 | 80 | 30 | 225 |
10 | 100 | 40 | 300 |
15 | 130 | 50 | 375 |
(a) Plot the points (4, 70), (6, 80), (10, 100), and so on in a Cartesian plane.
(b) Draw a line segment from the point (10, 100) to (30, 225). What does the slope of this line segment represent?
(c) Find the average rate of change of the monthly cost from 4 to 10 gigabytes.
(d) Find the average rate of change of the monthly cost from 10 to 30 gigabytes.
(e) Find the average rate of change of the monthly cost from 30 to 50 gigabytes.
(f) What is happening to the average rate of change as the gigabytes of data increase?
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