the function $f(t)$ represents the cost to connect to the internet at an online gaming store. it is a…

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.\nf(t)=\begin{cases}$0&0 < tleq30\\$5&30 < tleq90\\$10&t > 90end{cases}\nwhich statement is true about the internet connection cost?\no it costs $5 per hour to connect to the internet at the gaming store.\no the first half hour is free, and then it costs $5 per minute to connect to the internet.\no it costs $10 for each 90 minutes spent connected to the internet at the gaming store.\no any amount of time over an hour and a half would cost $10.

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.\nf(t)=\begin{cases}$0&0 < tleq30\\$5&30 < tleq90\\$10&t > 90end{cases}\nwhich statement is true about the internet connection cost?\no it costs $5 per hour to connect to the internet at the gaming store.\no the first half hour is free, and then it costs $5 per minute to connect to the internet.\no it costs $10 for each 90 minutes spent connected to the internet at the gaming store.\no any amount of time over an hour and a half would cost $10.

Answer

Answer:

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

Explanation:

Step1: Analyze time - cost intervals

The function $f(t)$ has three intervals. For $0 < t\leq30$ (30 minutes or half - hour), $f(t) = 0$. For $30 < t\leq90$ (from 30 minutes to 90 minutes or 1.5 hours), $f(t)=5$. For $t > 90$ (more than 90 minutes or 1.5 hours), $f(t)=10$.

Step2: Evaluate option A

In the interval $30 < t\leq90$, the cost is a flat $5$ for up to 60 minutes in this sub - interval, not $5$ per hour. So option A is incorrect.

Step3: Evaluate option B

The first 30 minutes are free, but for $30 < t\leq90$, the cost is a flat $5$ for this 60 - minute sub - interval, not $5$ per minute. So option B is incorrect.

Step4: Evaluate option C

For $t>90$, the cost is $10$ for any time over 90 minutes, not for each 90 minutes. So option C is incorrect.

Step5: Evaluate option D

Since an hour and a half is 90 minutes, and for $t > 90$, $f(t)=10$, any amount of time over an hour and a half would cost $10$. So option D is correct.