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.%0D%0ASelect all reasonable scales for the vertical axis.(3 points)%0D%0AResponses%0D%0A%0D%0A$1%0D%0A$1%0D%0A%0D%0A$5%0D%0A$5%0D%0A%0D%0A$25%0D%0A$25%0D%0A%0D%0A$50%0D%0A$50%0D%0A%0D%0A$100%0D%0A$100%0D%0A%0D%0A$400

Answer 1

To determine reasonable scales for the vertical axis when modeling the cost function \( t(d) = 50d + 200 \), we need to consider the output values of the function based on the number of days (\( d \)) for which a tuxedo is rented.

1. **Understanding the function**:
- The flat fee is $200.
- For each day rented, there is an additional charge of $50.

Thus, if you rent the tuxedo for different days, the costs will be as follows:
- For \( d = 0 \): \( t(0) = 50(0) + 200 = 200 \) (no rental days)
- For \( d = 1 \): \( t(1) = 50(1) + 200 = 250 \)
- For \( d = 2 \): \( t(2) = 50(2) + 200 = 300 \)
- For \( d = 3 \): \( t(3) = 50(3) + 200 = 350 \)
- For \( d = 4 \): \( t(4) = 50(4) + 200 = 400 \)

From this, we can derive the costs for renting the tuxedo for up to 4 days:
- At 0 days: $200
- At 1 day: $250
- At 2 days: $300
- At 3 days: $350
- At 4 days: $400

2. **Evaluating the potential scales**:
Given the function, reasonable vertical scales should allow for the costs shown above.

- **$1**: Not appropriate since costs are much higher than $1.
- **$5**: Not appropriate since costs start from $200.
- **$25**: Not appropriate, as the lowest reasonable cost starts from $200.
- **$50**: This could be reasonable as it allows for increments, but still not ideal.
- **$100**: This is reasonable since it allows for significant changes in the costs.
- **$400**: A reasonable scale as it aligns with the maximum described cost (for 4 days).

**Conclusion**: Reasonable vertical axis scales based on the above analysis for the function \( t(d) \) are \( $100 \) and \( $400 \). \(\$50\) could also be somewhat reasonable but is less ideal compared to \( \$100 \) and \( \$400 \). Scales like \( \$1, \$5, \) and \( \$25 \) are not suitable.