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 real life terms?
A. There is a cause of $0 for the first 10 miles.
B. The cost is $10 per mile.
C. There is a cost of $10 just to use the driving service.
D. There is a $0 service free for the first 10 miles.
Using m to represent miles and C(m) to represent the cost, what equation models the function in the table?
To find the rate of change/cost per mile driven, we can look at the difference in the costs for consecutive mile values.
The difference between the costs for 1 mile and 0 miles is $10.70 - $10 = $0.70.
The difference between the costs for 2 miles and 1 mile is $11.40 - $10.70 = $0.70.
The difference between the costs for 3 miles and 2 miles is $12.10 - $11.40 = $0.70.
The difference between the costs for 4 miles and 3 miles is $12.80 - $12.10 = $0.70.
Therefore, the rate of change/cost per mile driven is $0.70.
The first point (0, 10) in the table represents the cost of using the driving service for 0 miles driven. So:
D. There is a $0 service fee for the first 10 miles.
The equation that models this cost function is:
C(m) = 10 + (0.70)m