Certainly! Let's carefully break down each situation to define the appropriate functions:
1. Total salary as a function of the number of days worked:
- Situation: A person earns [tex]$750 per day.
- Function Definition: Let \( S(n) \) be the total salary where \( n \) is the number of days worked.
- Function:
\[
S(n) = 750n
\]
This means that the total salary \( S(n) \) is 750 multiplied by the number of days \( n \).
2. Computer rental fee as a function of the hours spent:
- Situation: A computer shop charges $[/tex]15 per hour.
- Function Definition: Let [tex]\( R(t) \)[/tex] be the computer rental fee where [tex]\( t \)[/tex] is the number of hours spent.
- Function:
[tex]\[
R(t) = 15t
\][/tex]
This means that the rental fee [tex]\( R(t) \)[/tex] is 15 multiplied by the number of hours [tex]\( t \)[/tex].
3. Parking fee as a function of the hours parked:
- Situation: The parking fee is [tex]$25 for the first 2 hours and an additional $[/tex]5 for each hour beyond that. If the time parked exceeds 12 hours, a flat rate of [tex]$100 applies.
- Function Definition: Let \( p(t) \) be the parking fee where \( t \) is the number of hours parked.
- Function:
\[
p(t) =
\begin{cases}
25 & \text{if } t \leq 2 \\
25 + 5(t - 2) & \text{if } 2 < t \leq 12 \\
100 & \text{if } t > 12
\end{cases}
\]
This function \( p(t) \) accounts for the different charges based on the hours parked: a flat $[/tex]25 for up to 2 hours, an additional [tex]$5 per hour for more than 2 but up to 12 hours, and a flat $[/tex]100 for more than 12 hours.
To summarize, the functions for each situation are:
1. [tex]\( S(n) = 750n \)[/tex]
2. [tex]\( R(t) = 15t \)[/tex]
3. [tex]\[
p(t) =
\begin{cases}
25 & \text{if } t \leq 2 \\
25 + 5(t - 2) & \text{if } 2 < t \leq 12 \\
100 & \text{if } t > 12
\end{cases}
\][/tex]
