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Let's break down the problem step by step:

1. **Given Information:**
   - The cost of the phone is **$175**.
   - The monthly plan costs **$74** per month.
   - Let $ t $ represent the number of months, and $ C(t) $ represent the total cost of the phone and the plan for $ t $ months.

2. **Formula for the function $ C(t) $:**
   The total cost consists of the one-time cost for the phone and the monthly charge for the plan. Therefore, the formula for the total cost $ C(t) $ after $ t $ months is:
   \[
   C(t) = 175 + 74t
   \]
   This equation accounts for the initial cost of the phone ($175) plus the monthly charge multiplied by the number of months ($74 * t$).

3. **Total cost for 12 months:**
   To find the total cost for 12 months, substitute $ t = 12 $ into the equation:
   \[
   C(12) = 175 + 74 \times 12 = 175 + 888 = 1063
   \]
   So, the total cost after 12 months is **$1063**.

### Final Answers:
- The formula is: $ C(t) = 175 + 74t $.
- The function notation for 12 months is: $ C(12) = 1063 $.
- The units are dollars.

Would you like further details or clarification?

Here are 5 related questions:
1. How would the formula change if the monthly cost increased?
2. What would be the cost for 6 months using the same formula?
3. Can you express the total cost after $ t $ months in terms of a percentage increase from the initial phone cost?
4. What happens to the total cost if the phone price is reduced by $25?
5. How would the cost change if the monthly fee dropped to $65 per month?

**Tip:** Always check if the question involves fixed costs (like the phone) versus recurring costs (like the monthly plan). This helps in writing the correct equation.

It's important to compare the total cost of cell phone plans including the cost of the phone. One company charges $175 for a phone and $74 per month for unlimited talk and text. Let C(t) represent the total cost of the phone and plan for t months. Give the formula for the function. What is the total cost for the plan for 12 months? Give the function notation in the first box, the answer in the second box, and choose the correct units in the third box.

Learn how to calculate the total cost of a cell phone plan using linear functions. This problem involves finding the total cost for a 12-month period, including a one-time phone charge and a monthly plan rate. Suitable for students in Grades 6-8.

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