Final answer:
The domain of M(n) is the set of whole numbers from 0 to 100, inclusive, representing the possible numbers of customers who can be present in the theater, with the maximum number restrained by the theater's seating capacity of 100.
Step-by-step explanation:
The domain of M(n) = 9n represents the set of all possible numbers of customers, n, that can be present in the local theater on Thursday night. Since the theater can hold a maximum of 100 customers and cannot have a negative number of customers, the domain of M(n) is all whole numbers from 0 to 100, inclusive. The domain is thus described using set notation as 0 ≤ n ≤ 100, n ∈ ℕ where ℕ represents the set of natural numbers including zero.
B) In this context, the domain for M(n) refers to the total number of customers, ranging from no customers (n=0) to a full house (n=100).
C) The range of values for n in the function M(n) is {0, 1, 2, ..., 100}.
D) Explaining the domain of M(n) with respect to the theater's capacity, it's crucial to acknowledge that the theater cannot admit more than 100 customers due to physical constraints and selling tickets beyond capacity is not possible. Therefore, the realistic domain reflects the fact that the number of tickets sold must be within the limits of the theater's seating capacity.