A taxi company charges $2.00 for the
first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 <� x <� 2
C(x) =
2.00 for 0 < x <= 1
2.00 + .20(10[x-1]) for 1 < x < 2
since there are 10 charging units per mile. The [x-1] is out there so you aren't charging for the first mile, and x=Overall miles. So [x-1]= miles going past the 1 mile.
To express the cost of a ride as a piecewise-defined function for a distance between 0 and 2 miles, we need to consider two situations:
1. When the distance x is less than or equal to 1 mile:
- The cost for the first mile (or part of a mile) is $2.00.
- There are no succeeding tenths of a mile, so there is no additional cost.
- Therefore, the cost C can be expressed as:
C = $2.00
2. When the distance x is greater than 1 mile but less than or equal to 2 miles:
- The cost for the first mile (or part of a mile) is $2.00.
- The cost for each succeeding tenth of a mile is $0.20.
- To determine the cost for the additional distance, we subtract 1 mile from x and multiply the resulting value by $0.20.
- Therefore, the cost C can be expressed as:
C = $2.00 + ($0.20 * (x - 1))
Combining these two situations, the piecewise-defined function for the cost C of a ride for 0 < x < 2 is:
C(x) = 2.00, 0 < x ≤ 1
C(x) = 2.00 + 0.20(x - 1), 1 < x ≤ 2
To express the cost C as a piecewise-defined function, we need to consider the different scenarios based on the distance traveled (0 < x < 2):
1. If x is less than or equal to 1 (0 < x ≤ 1), the cost will be a flat rate of $2.00. This is because the taxi company charges $2.00 for the first mile or part of a mile.
2. If x is greater than 1 (1 < x < 2), we need to calculate the cost for each succeeding tenth of a mile. The cost for each succeeding tenth of a mile is 20 cents, which is the same as $0.20.
Therefore, the piecewise-defined function for the cost C would be:
C(x) = { $2.00, if 0 < x ≤ 1
{ $2.00 + ($0.20 * (x - 1)), if 1 < x < 2
This function represents the cost C (in dollars) of a ride based on the distance x traveled (in miles) for 0 < x < 2.
C(x) =
2.00 for 0 < x <= 1
2.00 + .20(10x) for 1 < x < 2
since there are 10 charging units per mile.