Answer:
[tex]R(t)=\left\{\begin{matrix}20t; & 0\leq t\leq 2 \\ 20+10t; & 2 < t\end{matrix}\right.[/tex]
Step-by-step explanation:
Here, t represents the number of hours spent on using the computer,
Given,
The charge is 20 peso for first two hours,
Thus, if R(t) represents the total fee for using the computer,
[tex]R(t)=20t[/tex] for 0 ≤ t ≤ 2,
Also, after 2 hours the additional charges is 10 peso per hour,
For 2 hours the charges = 2 × 20 = 40 peso,
So, the charges for t hours for which t > 2,
[tex]R(t) = 40 + 10(t-2)[/tex]
[tex]=40+10t-20[/tex]
[tex]=20+10t[/tex]
Hence, the required function that represents the computer rental fee is,
[tex]R(t)=\left\{\begin{matrix}20t; & 0\leq t\leq 2 \\ 20+10t; & 2 < t\end{matrix}\right.[/tex]
The rental charges of the computer shop is an illustration of a piece-wise function.
The function for the computer rental fee is:
[tex]R(t) = \left \{ {{20t,\ \ 0 \le t\le 2} \atop {20 + 10t,\ \ t > 2}} \right.[/tex]
Given that:
[tex]t \to[/tex] number of hours
[tex]R(t) \to[/tex] Rental charges
The first 2 hours are charged at 20 pesos per hour.
So, we have:
[tex]R(t) = 20t,\ 0 \le t \le 2[/tex]
For hours greater than 2, the rate is calculated as follows:
Total = First 2 hours + 10 x Extra hours
So, we have:
[tex]R(t) = 20 \times 2 + 10 \times (t - 2)[/tex]
Open brackets
[tex]R(t) = 40+ 10t - 20[/tex]
Collect like terms
[tex]R(t) = 40- 20+ 10t[/tex]
[tex]R(t) = 20+ 10t[/tex]
Hence, the function is:
[tex]R(t) = \left \{ {{20t,\ \ 0 \le t\le 2} \atop {20 + 10t,\ \ t > 2}} \right.[/tex]
Read more about piecewise functions at:
https://brainly.com/question/12561612
