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?
Using m to represent miles and C(m) to represent the cost, what equation models the function in the table?
The rate of change/cost per mile driven is $0.70.
The first point (0, 10) represents the initial cost of the driving service, which is $10 even if the customer doesn't travel any distance.
The equation that models the function in the table is C(m) = 10 + 0.70m, where m is the number of miles driven and C(m) is the cost in dollars.
To find the rate of change/cost per mile driven, we can analyze the given table. We can observe that for each additional mile driven, the cost increases by $0.70. Therefore, the rate of change/cost per mile driven is $0.70.
In real-life terms, the point (0, 10) represents the initial cost that the driving service charges before any miles are driven. In this case, it is a flat fee of $10. So, if a passenger doesn't travel any distance and stays within a zero-mile radius, they will still be charged $10 for the service.
To model the function in the table using m to represent miles and C(m) to represent the cost, we can create an equation. Since the cost increases by $0.70 for each additional mile driven, we can use the slope-intercept form of a linear equation.
The equation for this scenario would be: C(m) = 10 + 0.70m
Where C(m) represents the cost of the driving service for m miles driven. The initial cost is represented by the y-intercept (10) and the rate of change/cost per mile driven is represented by the slope (0.70).
To find the rate of change/cost per mile driven, we can examine the difference in cost between two consecutive mile values.
Calculating the differences:
For 0 to 1 mile driven: 10.70 - 10 = 0.70
For 1 to 2 miles driven: 11.40 - 10.70 = 0.70
For 2 to 3 miles driven: 12.10 - 11.40 = 0.70
For 3 to 4 miles driven: 12.80 - 12.10 = 0.70
As we can see, for each additional mile driven, the cost increases by $0.70. Thus, the rate of change/cost per mile driven is $0.70.
The point (0,10) in real life terms represents the starting point of the journey, where the driver has not yet moved any distance but still has incurred a cost of $10. This is likely the base fare or initial cost of the service.
Using m to represent miles and C(m) to represent the cost, we can write the equation to model the function in the table as:
C(m) = 10 + 0.70m