Question

A hotel chain charges $75 each night for the first two nights and $50 for each additional night’s stay the total cost function T is a function of the number of nights x that a guest stays write the piecewise function T(x) and then calculate T(2) T(3) T(5)

Answer 1

We know that the hotel charges $75 for the first two nights. Thus, for x = 1 and x = 2, the cost is $75 each night. For x = 3 and any subsequent night, the cost is $50 each night.

Therefore, we can write the piecewise function T(x) as:

T(x) =
75 if x = 1 or x = 2,
50(x-2) if x ≥ 3.

Now let's calculate T(2), T(3), and T(5):

T(2) = 75 (as per the first condition of the piecewise function)

T(3) = 50(3-2) = 50 (as per the second condition of the piecewise function)

T(5) = 50(5-2) = 150 (as per the second condition of the piecewise function)