The cost $C$ of a taxi ride as a function of the distance $d$ traveled (in miles) can be expressed piecewise because the cost is structured differently for the first mile and for each subsequent part of a mile.

Key points:

1. The first mile (or part of a mile) costs $2.
2. For any distance beyond the first mile, each additional tenth of a mile (or part) costs 20 cents.

The function:

• For $0 < d \leq 1$ (i.e., the first mile or part of it), the cost is a flat $2.
• For $d > 1$, the cost is $2 for the first mile, plus an additional 20 cents for each tenth of a mile (or part) after the first mile. The number of such tenths is $10 \times (d - 1)$.

Thus, the cost function $C(d)$ can be expressed as:

\begin{cases} 2 & \text{if } 0 < d \leq 1, \\ 2 + 0.2 \times \lceil 10 \times (d - 1) \rceil & \text{if } d > 1, \end{cases}$$ where $$\lceil x \rceil$$ denotes the ceiling function, which rounds $$x$$ up to the nearest integer (since any part of a tenth of a mile also incurs a charge). ### Explanation: - For distances up to 1 mile, the cost is a flat $2. - For distances greater than 1 mile, we first subtract the initial mile ($$d - 1$$) and multiply by 10 to get the number of tenths of a mile. The ceiling function is used to ensure that any part of a tenth mile is charged as a full tenth. --- Do you want to go over how the ceiling function works in this context, or have any other questions? Here are 5 related questions: 1. What would be the cost for a 3.2-mile trip? 2. How does the ceiling function affect rounding in this pricing model? 3. Can you derive the cost for a trip of exactly 1.7 miles? 4. What is the cost for a trip of 5 miles? 5. How would you write a Python function to calculate the cost based on distance? **Tip**: In functions like these, ceiling and floor functions are often used to handle partial quantities that still incur full charges.