College Algebra, Chapter 3, 3.1, Section 3.1, Problem 78

Suppose a hotel chain charges \$75 each night for the first two nights and \$50 for each additional night's stay. The total cost $T$ is a function of the number of nights $x$ that a guest stays.
a.) Complete the expressions in the following Piecewise defined function.

$
T (x) = \left\{
\begin{array}{c}
\boxed{75x} & \text{if} & 0 \leq x \leq 2\\
\\
\boxed{50x+150} & \text{if} & x > 2
\end{array}
\right.
$

b.) Find $T(2)$, $T(3)$ and $T(5)$
Since $0 \leq 2 \leq 2$, then $T(2)= 75(2) = \$150 $
Since $3 > 2$, then $T(3) = 50(3) + 150 = \$300$
Since $5 > 2$, then $T(5) = 50(5) + 150 = \$400$

c.) What do your answers in part(b) represent?
The amount of rental charges depends on the number of nights that a guest stays.