A restaurant is open from 1 pm to 1 am on Saturday and a maximum of 110 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)?
To determine a reasonable domain and range for 𝑦 = 𝑓(𝑡), we need to consider the given information about the restaurant's opening hours and maximum capacity.
Domain: The domain represents the possible values for 𝑡, which represents the number of hours after 1 pm on Saturday. Since the restaurant is open from 1 pm to 1 am, it is open for a total of 12 hours. Therefore, a reasonable domain for 𝑡 would be the interval [0, 12]. This means that any value of 𝑡 between 0 and 12 (inclusive) can be used to represent the number of hours after 1 pm.
Range: The range represents the values that 𝑦 (which corresponds to the number of people in the restaurant) can take. Given that the maximum capacity of the restaurant is 110 people, it would be reasonable to expect the range of 𝑦 to be the interval [0, 110] (inclusive). This means that 𝑦 can take any value between 0 and 110 (inclusive) inclusively, representing the possible number of people in the restaurant at any given time.
In summary, a reasonable domain for 𝑡 is [0, 12] and a reasonable range for 𝑦 is [0, 110].