A restaurant is open from 1 pm to 1 am on Saturday and a maximum of 140 people are allowed inside. If f(t) is the number of people in the restaurant t hours after 1 pm on Saturday, what is a reasonable domain and range for y=f(t)?
D: [0,12]
R: [0,140]
To determine the reasonable domain and range for the function f(t), let's consider the given information.
1) The restaurant is open from 1 pm to 1 am, which is a total of 12 hours.
2) The maximum number of people allowed inside is 140.
Based on this information, we can determine the domain and range as follows:
1) Domain: The domain represents the valid values for the input variable, which in this case is time (t) in hours. Since the restaurant is open from 1 pm to 1 am, the reasonable domain for t would be from 0 to 12 (inclusive). We start at 0 hours because 1 pm corresponds to t = 0, and we end at 12 hours because 1 am corresponds to t = 12.
Therefore, the domain for f(t) would be: 0 ≤ t ≤ 12.
2) Range: The range represents the possible values for the output variable, which in this case is the number of people (f(t)) in the restaurant. We know that the maximum number of people allowed inside is 140. So, the range for f(t) would be from 0 to 140 (inclusive) since it is reasonable to assume that the number of people cannot be negative and cannot exceed the maximum capacity.
Therefore, the range for f(t) would be: 0 ≤ f(t) ≤ 140.
In summary, a reasonable domain for t would be 0 ≤ t ≤ 12, and a reasonable range for f(t) would be 0 ≤ f(t) ≤ 140.