In 2014, the United States Postal Service charged $0.48 to mail a first class letter weighing upto 1oz. And $0.21 for each additional ounce. Based on these rates which function would determine the cost, in dollars, c(z), of meiling a first-class letter weighing z ounces where z is an integer greater than 1?

Options

A. `c(z)=0.48z+0.21`
B. `c(z)=0.21z+0.48`
C. `c(z)=0.48(z-1)+0.21`
D. `c(z)=0.21(z-1)+0.48`

Answer

To determine the cost, in dollars, \( c(z) \), of mailing a first-class letter weighing \( z \) ounces (where \( z \) is an integer greater than 1), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Pricing Structure**:
- The cost to mail a first-class letter weighing up to 1 ounce is $0.48.
- For each additional ounce beyond the first ounce, there is an additional charge of $0.21.

2. **Identify the Weight for Additional Charges**:
- Since the first ounce is covered by the initial charge of $0.48, we only need to consider the weight beyond the first ounce.
- Therefore, if the letter weighs \( z \) ounces, the additional weight that incurs a charge is \( z - 1 \) ounces.

3. **Calculate the Additional Cost**:
- For each additional ounce beyond the first, the cost is $0.21.
- Thus, the total additional cost for \( z - 1 \) ounces is given by:
\[ 0.21 \times (z - 1) \]

4. **Combine the Base Cost and Additional Cost**:
- The total cost \( c(z) \) can be expressed as the sum of the base cost and the additional cost:
\[ c(z) = 0.48 + 0.21 \times (z - 1) \]

5. **Simplify the Expression**:
- Distributing the $0.21:
\[ c(z) = 0.48 + 0.21z - 0.21 \]
- Combining like terms:
\[ c(z) = 0.21z + 0.27 \]

### Final Function:
Thus, the function that determines the cost of mailing a first-class letter weighing \( z \) ounces is:
\[ c(z) = 0.21z + 0.27 \]