To determine reasonable scales for the vertical axis when modeling the cost function \( t(d) = 50d + 200 \), we first need to consider the values that \( t(d) \) can take based on a sensible range of \( d \) (number of days).
-
When \( d = 0 \) (no days rented):
\[ t(0) = 50(0) + 200 = 200 \] -
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 \( d = 4 \):
\[ t(4) = 50(4) + 200 = 400 \]
Considering these calculations, we can see that the cost starts at $200 and increases by $50 for each additional day rented. Therefore, the total cost at reasonable values for \( d \) such as 0 to 4 days ranges from $200 to $400.
Possible scales for the vertical axis should be reasonable increments that could include these values. The following are considered:
- $1: Too small for practical application; minor increments won’t help in understanding the data.
- $5: Still too small; it would create a cluttered graph for real values.
- $25: Reasonable, as costs will vary significantly in this range.
- $50: Also reasonable, particularly since the daily charge is $50.
- $100: Reasonable, allowing a clear view as the values will reach $400.
- $400: It's one of the potential values but provides limited intermediate scales.
In summary, the reasonable scales for the vertical axis based on our analysis would be:
- $25
- $50
- $100
- $400
The scales of $1 and $5 are too small and not practical for this cost model. Therefore, the appropriate selections are $25, $50, $100, and $400.