To determine the cost of an [tex]\( n \)[/tex]-minute long distance call, we need to derive a mathematical expression based on the given data in the table. Let's go through the steps together:
1. Understand the pattern in the table:
- For a 5-minute call, the cost is [tex]$0.55.
- For a 6-minute call, the cost is $[/tex]0.62.
- For a 7-minute call, the cost is [tex]$0.69.
- For an 8-minute call, the cost is $[/tex]0.76.
- For a 9-minute call, the cost is [tex]$0.83.
- For a 10-minute call, the cost is $[/tex]0.90.
2. Determine the incremental cost:
- Notice how the cost increases as the call duration increases by one minute.
- The incremental cost per additional minute is constant. For example:
- From 5 to 6 minutes, the cost increases by [tex]$0.07 ($[/tex]0.62 - [tex]$0.55).
- From 6 to 7 minutes, it increases by $[/tex]0.07 ([tex]$0.69 - $[/tex]0.62).
- This same increase of [tex]$0.07 applies for each additional minute.
3. Formulate the expression:
- The base cost for the first 5 minutes is $[/tex]0.55.
- Each additional minute beyond the initial 5 minutes incurs an extra cost of $0.07.
- Therefore, for a call lasting [tex]\( n \)[/tex] minutes, where [tex]\( n \)[/tex] is at least 5, the extra cost due to the additional [tex]\( n - 5 \)[/tex] minutes is [tex]\( (n - 5) \times 0.07 \)[/tex].
4. Write the expression:
- The cost of an [tex]\( n \)[/tex]-minute call can be written as the sum of the base cost and the incremental costs.
- Thus, the expression for the cost [tex]\( a(n) \)[/tex] of an [tex]\( n \)[/tex]-minute call is:
[tex]\[
a(n) = 0.55 + (n - 5) \times 0.07
\][/tex]
This matches with the expression provided, which is:
[tex]\[
a(n) = 0.55 + (n - 5) \times 0.07
\][/tex]
Therefore, the expression that can be used to find the cost of an [tex]\( n \)[/tex]-minute long distance call, where [tex]\( n \)[/tex] is at least 5 minutes, is:
[tex]\[
a(n) = 0.55 + (n - 5) \times 0.07
\][/tex]
Among the given options, this is equivalent to:
[tex]\[ a(n) = 0.55 + (n - 5) \times 0.07 \][/tex]
