Darell tutors at a neighborhood community center after school. He charges $20 for an hour-long tutoring session. The function P(t) represents the total amount, in dollars, that Darell earns for providing t tutoring sessions.
What is the domain of P(t)?
The domain of P(t) represents all possible values that t can take. In this case, t represents the number of tutoring sessions. Since the number of tutoring sessions cannot be negative or a fraction (it must be a positive integer), the domain of P(t) is the set of all positive integers or {1, 2, 3, ...}.
The domain of a function refers to the set of all possible input values. In the given context, the input represents the number of tutoring sessions, denoted by t. However, there are no specific restrictions mentioned in the problem statement regarding the maximum or minimum number of tutoring sessions.
Therefore, we can assume that the domain of the function P(t) is all real numbers. Hence, the domain of P(t) is (-∞, ∞).
The domain of a function represents all possible input values for the function. In this case, the function P(t) represents the total amount earned by Darell for providing t tutoring sessions.
Since the number of tutoring sessions, t, can be any positive whole number (e.g., 1, 2, 3, ...), the domain of P(t) would also be any positive whole number. However, it is important to note that the domain cannot be negative or zero values, as you cannot have a negative or zero number of tutoring sessions.
So, the domain of P(t) would be the set of positive integers, excluding zero.
In mathematical notation, the domain of P(t) can be represented as:
Domain(P) = {t | t ∈ Z⁺, t ≠ 0}