Question

A taxi company charges $4.00 for the first mile (or part of a mile ) and 80 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.

Answer 1

To express the cost of a ride as a piecewise defined function of the distance traveled, we need to consider the rates for different distance ranges. For 0 < x <= 1 mile, the cost is $4.00. For 1 < x <= 2 miles, we calculate the number of tenths of a mile in that range and multiply it by 0.80 to find the additional cost.

Step-by-step explanation:

To express the cost C of a ride as a piecewise defined function of the distance x traveled, we need to consider the different rates for the first mile and each succeeding tenth of a mile. Let's break it down:

For 0 < x ≤ 1 (up to 1 mile), the cost is $4.00.

For 1 < x ≤ 2 (between 1 and 2 miles), we need to calculate the number of tenths of a mile in this range. For example, if x = 1.8, there are 8 tenths of a mile. Multiply the number of tenths by 0.80 to calculate the additional cost. So, for x = 1.8, the additional cost would be 8 * 0.80 = $6.40.

Therefore, the piecewise defined function for the cost C (in dollars) of a ride for 0 < x ≤ 2 is:

C(x) = $4.00 for 0 < x ≤ 1, and C(x) = $4.00 + (x - 1) * 0.80 for 1 < x ≤ 2.