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?
The rate of change/cost per mile driven can be found by calculating the difference in cost between two consecutive values and dividing it by the difference in miles driven.
The difference in cost between 1 mile and 0 miles driven is $10.70 - $10 = $0.70.
The difference in miles driven between 1 mile and 0 miles driven is 1 - 0 = 1.
Therefore, the rate of change/cost per mile driven is $0.70 / 1 = $0.70.
What does the first point (0, 10) represent in the context of the problem?
In the context of the problem, the first point (0, 10) represents the starting point or the cost of the service when no miles are driven. It indicates that regardless of the distance traveled, there is a fixed cost of $10.
Using m to represent miles and C(m) to represent the cost, what equation models the function in the table?
The equation that models the function in the table can be determined by observing the pattern in the cost as the miles driven increases.
From the table, we can see that the cost increases by $0.70 for every 1 mile driven. Therefore, the equation can be written as:
C(m) = $10 + $0.70 * m
Where:
C(m) represents the cost for driving m miles.
To find the rate of change or cost per mile driven, we need to figure out how the cost changes for every additional mile. We can do this by looking at the differences in cost between consecutive miles.
Let's calculate the differences in cost for each additional mile:
Cost for 1 mile - Cost for 0 miles = 10.70 - 10.00 = 0.70
Cost for 2 miles - Cost for 1 mile = 11.40 - 10.70 = 0.70
Cost for 3 miles - Cost for 2 miles = 12.10 - 11.40 = 0.70
Cost for 4 miles - Cost for 3 miles = 12.80 - 12.10 = 0.70
As we can see, the price increases by $0.70 for every additional mile driven.
So, the rate of change or cost per mile driven is $0.70.