Question

A tuxedo rental company charges a flat fee of $200 plus $50 per day to rent one of their tuxedos. The function that models the cost to rent the tutus 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
$1
$5
$25
$50
$100
$400

Answer 1

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

1. For \( d = 0 \) (no rental days),
\[
t(0) = 50(0) + 200 = 200
\]

2. For \( d = 1 \) (one rental day),
\[
t(1) = 50(1) + 200 = 250
\]

3. For \( d = 2 \) (two rental days),
\[
t(2) = 50(2) + 200 = 300
\]

4. For \( d = 3 \) (three rental days),
\[
t(3) = 50(3) + 200 = 350
\]

5. For \( d = 4 \) (four rental days),
\[
t(4) = 50(4) + 200 = 400
\]

From this, you can see that the total cost increases linearly depending on \( d \). The function starts at $200 when \( d = 0 \) and increases by $50 for each additional day.

Considering the range of values:
- The minimum value is $200 (for \( d = 0 \)).
- The values for \( d = 1, 2, 3, 4 \) give us costs of $250, $300, $350, and $400 respectively.

Now, looking at your provided scale options:
- $1: Too small.
- $5: Too small.
- $25: Too small.
- $50: Reasonable, as it can show the incremental daily cost.
- $100: Reasonable, as it captures larger increments.
- $400: Reasonable, as it is a possible maximum rental cost for \( d = 4 \).

Thus, **the reasonable scales for the vertical axis** are:
- $50
- $100
- $400