Question

the cost of a single ticket depends on the number of tickets, t, purchased in a group, as represented by the function c(t).
c(t) = \

$$\begin{cases} \\$ 18.50, & 1 \\leq t < 12 \\\\ \\$ 16.00, & 12 \\leq t < 20 \\\\ \\$ 14.50, & 20 \\leq t \\end{cases}$$

what is the total cost for 20 tickets?
\bigcirc \\$14.50
\bigcirc \\$16.00
\bigcirc \\$290.00
\bigcirc \\$320.00

Explanation:

Step1: Determine the cost per ticket for 20 tickets

For \( t = 20 \), we check the piecewise function. The condition \( 20\leq t \) applies, so the cost per ticket \( C(20)=\$14.50 \).

Step2: Calculate total cost for 20 tickets

Total cost is cost per ticket times number of tickets. So total cost \( = 14.50\times20 \).
\( 14.50\times20 = 290 \).

Answer:

\$290.00