A taxi company charges $3.00 for the first mile (or part of a mile) and 60 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) =
___________ if 0 < x ≤ 1
___________ if 1 < x ≤ 1.1
___________ if 1.1 < x ≤ 1.2
___________ if 1.9 < x ≤ 2
To express the cost C(x) as a piecewise defined function of the distance x, we need to consider the different cases based on the given conditions.
Case 1: 0 < x ≤ 1
For this case, the cost is $3.00 for the first mile or part of a mile. Since x is in the range of 0 to 1, the cost will be a flat rate of $3.00.
Therefore, the expression for this case is C(x) = $3.00.
Case 2: 1 < x ≤ 1.1
In this case, the distance traveled is between 1 and 1.1 miles. The initial $3.00 is still applicable, and for the additional tenth of a mile, the cost is 60 cents. As there is only one tenth of a mile, the cost will be $3.60.
Therefore, the expression for this case is C(x) = $3.60.
Case 3: 1.1 < x ≤ 1.2
For distances between 1.1 and 1.2 miles, we have the initial $3.00 plus two tenths of a mile. Each tenth of a mile costs 60 cents, so two tenths would cost $1.20. Adding this to the initial $3.00 gives us a cost of $4.20.
Therefore, the expression for this case is C(x) = $4.20.
Case 4: 1.9 < x ≤ 2
Lastly, for distances between 1.9 and 2 miles, we have the initial $3.00 plus nine tenths of a mile. Nine tenths at 60 cents per tenth of a mile gives us $5.40. Adding this to the initial $3.00 gives us a cost of $8.40.
Therefore, the expression for this case is C(x) = $8.40.
Now, let's summarize the expressions for each case:
C(x) = $3.00 if 0 < x ≤ 1
C(x) = $3.60 if 1 < x ≤ 1.1
C(x) = $4.20 if 1.1 < x ≤ 1.2
C(x) = $8.40 if 1.9 < x ≤ 2
These expressions represent the cost C(x) in dollars as a piecewise defined function of the distance x traveled in the given range 0 < x ≤ 2.