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 \( t = 20 \), we use the piece of the function where \( 20\leq t \). So the cost per ticket \( C(20)=\$14.50 \).

Step2: Calculate total cost

Total cost is the cost per ticket times the number of tickets. So total cost \( = 14.50\times20 \).
\( 14.50\times20 = 290.00 \)

Answer:

\(\$290.00\) (corresponding to the option with \(\$290.00\))