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.

Question

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.