A driving service, like Uber or Lyft, charges the following, as modeled in the table, per mile driven.
Miles Driven Cost
0 $10
1 10.70
2 11.40
3 12.10
4 12.80
What is the rate of change/cost per mile driven?
What does the first point (0, 10) represent in the context of the problem?
Using m to represent miles and C(m) to represent the cost, what equation models the function in the table?
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The rate of change/cost per mile driven can be determined by finding the difference in the cost for consecutive miles driven.
For example, the cost for driving 1 mile is $10.70, while the cost for driving 0 miles is $10. The difference between these two costs is $10.70 - $10 = $0.70.
Therefore, the rate of change/cost per mile driven is $0.70.
In the context of the problem, the first point (0, 10) represents the cost of not driving any miles. It indicates that the base cost for using the driving service, regardless of the number of miles driven, is $10.
The equation that models the function in the table can be expressed as:
C(m) = 10 + 0.70m
Here, m represents the number of miles driven, and C(m) represents the total cost for driving that many miles. The equation takes into account the base cost of $10 and the rate of change/cost per mile driven of $0.70.