Gina subscribes to a cell phone service that charges a monthly fee of `$60.00`. The first 500 megabytes of data is free, and the cost is `$0.15` for each additional megabyte of data used that month. Which of the following functions gives the cost, in dollars, for a month in which Gina uses x megabytes of data, where `x gt 500`.

Options

A. `60+15x`
B. `0.15x-15`
C. `0.15x-440`
D. `60+0.15x`

Answer

To find the cost function for Gina's cell phone service when she uses more than 500 megabytes (MB) of data, we can break down the problem step by step.

### Step 1: Identify the fixed cost
Gina has a monthly fee of $60. This is a fixed cost that she pays regardless of her data usage.

**Hint:** Remember that fixed costs do not change with the level of service used.

### Step 2: Determine the free data allowance
The first 500 MB of data is free. This means that if Gina uses up to 500 MB, she will not incur any additional charges.

**Hint:** Free allowances can significantly affect the total cost, so always account for them first.

### Step 3: Calculate additional data usage
Since Gina uses more than 500 MB, we need to calculate how much additional data she uses. If she uses `x` MB, the additional data used is given by:
\[ \text{Additional Data} = x - 500 \]

**Hint:** Always subtract the free allowance from the total usage to find the additional cost.

### Step 4: Determine the cost of additional data
The cost for each additional MB used beyond the free 500 MB is $0.15. Therefore, the total cost for the additional data is:
\[ \text{Cost of Additional Data} = 0.15 \times (x - 500) \]

**Hint:** Multiplying the additional data by the cost per MB gives the total additional cost.

### Step 5: Formulate the total cost function
Now, we can combine the fixed cost and the cost of additional data to get the total cost function:
\[ \text{Total Cost} = \text{Fixed Cost} + \text{Cost of Additional Data} \]
Substituting the values we have:
\[ \text{Total Cost} = 60 + 0.15(x - 500) \]

### Step 6: Simplify the cost function
Now we simplify the expression:
\[ \text{Total Cost} = 60 + 0.15x - 0.15 \times 500 \]
Calculating \(0.15 \times 500\):
\[ 0.15 \times 500 = 75 \]
So, we have:
\[ \text{Total Cost} = 60 + 0.15x - 75 \]
Combining the constant terms:
\[ \text{Total Cost} = 0.15x + (60 - 75) = 0.15x - 15 \]

### Final Cost Function
Thus, the cost function for Gina when she uses more than 500 MB is:
\[ \text{Cost} = 0.15x - 15 \]

### Conclusion
From the provided options, the correct function that represents the cost in dollars for a month in which Gina uses \(x\) megabytes of data (where \(x > 500\)) is:
**Option 2: \(0.15x - 15\)**.

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