Question

the function f(t) represents the cost to connect to the internet at an online gaming store. it is a function of t, the time in minutes spent on the internet.
$f(t)=\

$$\begin{cases} \\$0 & 0 < t \\leq 30 \\\\ \\$5 & 30 < t \\leq 90 \\\\ \\$10 & t > 90 \\end{cases}$$

$
which statement is true about the internet connection cost?
\bigcirc it costs \\$5 per hour to connect to the internet at the gaming store.
\bigcirc the first half hour is free, and then it costs \\$5 per minute to connect to the internet.
\bigcirc it costs \\$10 for each 90 minutes spent connected to the internet at the gaming store.
\bigcirc any amount of time over an hour and a half would cost \\$10.

Explanation:

Step1: Analyze each option

• Option 1: Check cost per hour. For \(10 < t \leq 90\) (up to 90 minutes, 1.5 hours), cost is $5. So per hour, it's not $5 (since $5 for 1.5 hours is less than $5 per hour). Eliminate.
• Option 2: First 10 minutes (not half - hour) is $0, then cost is $5 for the entire interval \(10 < t \leq 90\), not per minute. Eliminate.
• Option 3: For \(t>90\), cost is $10, not for each 90 minutes. Eliminate.
• Option 4: An hour and a half is 90 minutes. For \(t > 90\), cost is $10. So any time over 90 minutes (an hour and a half) costs $10. This is correct.

Answer:

Any amount of time over an hour and a half would cost $10.