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)

1 answer

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.