Question

c(x) = \

$$\begin{cases} 100 & 0 < x \\leq 10 \\\\ 200 & 10 < x \\leq 20 \\\\ 300 & 20 < x \\leq 30 \\end{cases}$$

function c is the cost for x, amount of people to enter the park. what is the cost if x = 22 ? options: 300, 200, undefined, 100

Explanation:

Step1: Identify the interval for x=22

Check which piecewise function interval \( 22 \) falls into. The intervals are \( 0 < x \leq 10 \), \( 10 < x \leq 20 \), \( 20 < x \leq 30 \). Since \( 20 < 22 \leq 30 \), we use the third piece.

Step2: Determine the cost from the function

For \( 20 < x \leq 30 \), the function \( C(x) = 300 \). So when \( x = 22 \), \( C(22) = 300 \).

Answer:

300