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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
$400
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1 answer

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

  1. If \( d = 0 \) (renting for 0 days), the cost \( t(0) = 50(0) + 200 = 200 \).
  2. If \( d = 1 \) (renting for 1 day), the cost \( t(1) = 50(1) + 200 = 250 \).
  3. If \( d = 2 \) (renting for 2 days), the cost \( t(2) = 50(2) + 200 = 300 \).
  4. If \( d = 3 \) (renting for 3 days), the cost \( t(3) = 50(3) + 200 = 350 \).
  5. If \( d = 4 \) (renting for 4 days), the cost \( t(4) = 50(4) + 200 = 400 \).
  6. If \( d = 5 \) (renting for 5 days), the cost \( t(5) = 50(5) + 200 = 450 \).

From these calculations, the function produces costs starting at $200 and increasing by $50 for each subsequent day rented. Based on the costs calculated (250, 300, 350, 400, 450, etc.), the potential values for \( t(d) \) for reasonable rental durations can be up to around $400 and beyond, depending on how many days are rented.

Therefore, reasonable scales for the vertical axis, considering this information, would include values where the costs fall, particularly focusing primarily on those between $200 and higher amounts based on specific increments.

Considering the provided options:

  • $100: Yes, because values will exceed $200.
  • $200: This is a starting point.
  • $400: This is a valid cost for renting for 4 days.

The most appropriate options from the provided choices for a reasonable scale on the vertical axis would be $100, $400, and possibly even $25 or $50, depending on the graph's detail level, but the key values that should certainly be included in the scale are those directly related to the cost function itself as described above.