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?
The rate of change or cost per mile driven can be found by calculating the difference in cost between consecutive distances and dividing it by the difference in miles driven.
Rate of change = (change in cost) / (change in miles driven)
For example, the rate of change between 0 miles and 1 mile is (10.70 - 10) / (1 - 0) = 0.70.
The first point in the table (0, 10) represents the base cost or initial charge for the driving service. In this case, when the miles driven is 0, the cost is $10.
The equation that models the function in the table can be written as:
C(m) = 10 + 0.70m