Question

A tuxedo rental company charges a flat fee of $200 plus a $50 per day fee to rent one of their tuxedos. The function that models the cost to rent a tuxedo is t(d)=50d+200, where d represents the number of days in which the tuxedo is rented and t represents the total cost of the rental.
Select all reasonable scales for the vertical axis.(3 points)

Answer 1

To determine reasonable scales for the vertical axis (cost, \( t \)) based on the function \( t(d) = 50d + 200 \), we can examine the cost values for different numbers of rental days, \( d \).

1. **Calculate the minimum cost**:
- When \( d = 0 \) days:
\[
t(0) = 50(0) + 200 = 200
\]
So, the minimum cost is $200.

2. **Calculate additional costs for different \( d \) values**:
- When \( d = 1 \):
\[
t(1) = 50(1) + 200 = 250
\]
- When \( d = 2 \):
\[
t(2) = 50(2) + 200 = 300
\]
- When \( d = 3 \):
\[
t(3) = 50(3) + 200 = 350
\]
- When \( d = 4 \):
\[
t(4) = 50(4) + 200 = 400
\]
- When \( d = 5 \):
\[
t(5) = 50(5) + 200 = 450
\]
- When \( d = 6 \):
\[
t(6) = 50(6) + 200 = 500
\]

3. **Generate a reasonable range for the vertical axis**:
- The minimum cost is $200, and additional costs will keep increasing in increments of $50 for each day rented.
- If we consider costs for up to 10 days:
- When \( d = 10 \):
\[
t(10) = 50(10) + 200 = 700
\]

Therefore, the reasonable cost range could be from $200 (for 0 days) to $700 (for 10 days).

### Reasonable Vertical Axis Scales:
- A reasonable range for the vertical axis can be between $200 and $700, with increments of $50, such as:
- $200, $250, $300, $350, $400, $450, $500, $550, $600, $650, $700.

Thus, possible scales for the vertical axis could be:
- 200
- 250
- 300
- 350
- 400
- 450
- 500
- 550
- 600
- 650
- 700

Selecting a scale that captures all feasible costs within that range is important for accurately representing the function on a graph. The increments of $50 are suitable as they align with the per-day cost.