Question

15. 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)
Responses

$1
$1

$5
$5

$25
$25

$50
$50

$100
$100

$400

Answer 1

To determine reasonable scales for the vertical axis when modeling the cost function \( t(d) = 50d + 200 \), we first need to consider the values that \( t(d) \) can take based on a sensible range of \( d \) (number of days).

1. **When \( d = 0 \)** (no days rented):
\[ t(0) = 50(0) + 200 = 200 \]

2. **When \( d = 1 \)**:
\[ t(1) = 50(1) + 200 = 250 \]

3. **When \( d = 2 \)**:
\[ t(2) = 50(2) + 200 = 300 \]

4. **When \( d = 3 \)**:
\[ t(3) = 50(3) + 200 = 350 \]

5. **When \( d = 4 \)**:
\[ t(4) = 50(4) + 200 = 400 \]

Considering these calculations, we can see that the cost starts at $200 and increases by $50 for each additional day rented. Therefore, the total cost at reasonable values for \( d \) such as 0 to 4 days ranges from $200 to $400.

**Possible scales for the vertical axis** should be reasonable increments that could include these values. The following are considered:

- **$1**: Too small for practical application; minor increments won’t help in understanding the data.
- **$5**: Still too small; it would create a cluttered graph for real values.
- **$25**: Reasonable, as costs will vary significantly in this range.
- **$50**: Also reasonable, particularly since the daily charge is $50.
- **$100**: Reasonable, allowing a clear view as the values will reach $400.
- **$400**: It's one of the potential values but provides limited intermediate scales.

In summary, **the reasonable scales for the vertical axis** based on our analysis would be:

- **$25**
- **$50**
- **$100**
- **$400**

The scales of **$1** and **$5** are too small and not practical for this cost model. Therefore, the appropriate selections are **$25**, **$50**, **$100**, and **$400**.