To determine reasonable scales for the vertical axis when modeling the cost function \( t(d) = 50d + 200 \), we need to consider the output values of the function based on the number of days (\( d \)) for which a tuxedo is rented.
- Understanding the function:
- The flat fee is $200.
- For each day rented, there is an additional charge of $50.
Thus, if you rent the tuxedo for different days, the costs will be as follows:
- For \( d = 0 \): \( t(0) = 50(0) + 200 = 200 \) (no rental days)
- For \( d = 1 \): \( t(1) = 50(1) + 200 = 250 \)
- For \( d = 2 \): \( t(2) = 50(2) + 200 = 300 \)
- For \( d = 3 \): \( t(3) = 50(3) + 200 = 350 \)
- For \( d = 4 \): \( t(4) = 50(4) + 200 = 400 \)
From this, we can derive the costs for renting the tuxedo for up to 4 days:
- At 0 days: $200
- At 1 day: $250
- At 2 days: $300
- At 3 days: $350
- At 4 days: $400
- Evaluating the potential scales: Given the function, reasonable vertical scales should allow for the costs shown above.
- $1: Not appropriate since costs are much higher than $1.
- $5: Not appropriate since costs start from $200.
- $25: Not appropriate, as the lowest reasonable cost starts from $200.
- $50: This could be reasonable as it allows for increments, but still not ideal.
- $100: This is reasonable since it allows for significant changes in the costs.
- $400: A reasonable scale as it aligns with the maximum described cost (for 4 days).
Conclusion: Reasonable vertical axis scales based on the above analysis for the function \( t(d) \) are \( $100 \) and \( $400 \). \($50\) could also be somewhat reasonable but is less ideal compared to \( $100 \) and \( $400 \). Scales like \( $1, $5, \) and \( $25 \) are not suitable.
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