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.