The fare of a taxi ride starts at $2.50 and increases by $4.15 per km, for the first 5.5 km. After 5.5 km the rate charged per km decreases by $0.50.
Write down a piecewise function that models the fare of the taxi ride and show that the function is continuous when the taxi ride reaches 5.5 km.
Calculate the distance of a taxi ride that costs $15.
On a particular ride, a taxi driver accidentally takes a wrong turn 2.8 km into the ride that extends the journey by 2.1 km. Since the driver cannot switch off the fare calculator in the taxi without losing the details of the ride he decides to calculate the fair price for his customer, by removing the cost from the extra distance travelled. The total length of the journey, including the 2.1 km detour, was 9.4 km.
Calculate the proper fare the customer should pay, having appropriately discounted the distance of the detour.
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