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, \( d \).
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Calculate the minimum cost:
- When \( d = 0 \) days: \[ t(0) = 50(0) + 200 = 200 \] So, the minimum cost is $200.
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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 \( d = 6 \): \[ t(6) = 50(6) + 200 = 500 \]
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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.