To analyze the cost structure in the table provided, let's break down the information given:
- For 1 month, the total cost is $52.
- For 2 months, the total cost is $74.
- For 3 months, the total cost is $96.
From this data, we can determine the initial cost and the monthly cost:
Step 1: Find the Initial Cost
The cost appears to have a fixed initial start-up fee followed by a regular monthly fee. We can analyze the differences between the costs for consecutive months to find out the monthly fee.
- The cost from 1 month to 2 months increases from $52 to $74, which is an increase of $22.
- The cost from 2 months to 3 months increases from $74 to $96, which is also an increase of $22.
This suggests that the monthly cost is $22.
Step 2: Calculate the Initial Cost
Now that we know the monthly cost, we can calculate the initial cost:
Let \( x \) be the initial cost and \( m \) be the monthly cost. From the data above,
-
For 1 month: \( x + m = 52 \)
Thus, with \( m = 22 \): \[ x + 22 = 52 \implies x = 52 - 22 = 30 \]
So, the initial cost is $30.
Summary:
- The cost per month is $22.
- The initial cost is $30.