Question

A bicycle rental company charges $3 up front and $1 for every 15 minutes thereafter. Which graph best represents the cost of the bicycle rental over time.

Answer 1

To represent the cost of a bicycle rental over time with a starting fee and a charge based on time, we can break down the pricing structure as follows:

1. **Initial Fee**: There is an upfront cost of $3.
2. **Subsequent Fees**: After the first 15 minutes, the cost increases by $1 for every additional 15-minute interval.

We can create a cost function based on time \( t \) in minutes:

- For 0 to 15 minutes, the cost is constant at $3.
- For each additional 15-minute interval, the cost increases by $1.

The breakdown is:

- 0 to 15 minutes: Cost = $3
- 15 to 30 minutes: Cost = $4
- 30 to 45 minutes: Cost = $5
- 45 to 60 minutes: Cost = $6
- And so on...

For each interval, the cost can be represented as:
\[ \text{Cost} = 3 + \left\lfloor \frac{t - 1}{15} \right\rfloor \]

This means:
- For \( 0 < t \leq 15 \): Cost = $3
- For \( 15 < t \leq 30 \): Cost = $4
- For \( 30 < t \leq 45 \): Cost = $5
- For \( 45 < t \leq 60 \): Cost = $6, etc.

On a graph, this would show as a step function, starting at \( (0, 3) \) and then having horizontal steps that increase at each 15-minute interval.

If you have multiple choice graphs, look for a graph that:
- Starts at 3 on the y-axis when t = 0.
- Has horizontal segments that represent the cost remaining the same for each 15-minute interval, then jumping up by $1 at each 15-minute mark.

This would illustrate the cost structure clearly.