Question

. A local moving company charges a flat fee of $500 for the first 3 hours of all moves and $100 for each additional hour. The moving company uses the formula M(t)=100(t−3)+500, when t>3 to determine the cost of each move, M, based on the amount of time needed, t, in hours.

Using the equation, complete the given table.

Answer 1

To fill out the table using the moving company's pricing formula \( M(t) = 100(t - 3) + 500 \) for \( t > 3 \), we will calculate the cost for various values of \( t \).

Let's assume we need to fill out the table for the following values of \( t \): 4, 5, 6, 7, 8.

### Calculations:
1. **For \( t = 4 \)**:
\[
M(4) = 100(4 - 3) + 500 = 100(1) + 500 = 100 + 500 = 600
\]

2. **For \( t = 5 \)**:
\[
M(5) = 100(5 - 3) + 500 = 100(2) + 500 = 200 + 500 = 700
\]

3. **For \( t = 6 \)**:
\[
M(6) = 100(6 - 3) + 500 = 100(3) + 500 = 300 + 500 = 800
\]

4. **For \( t = 7 \)**:
\[
M(7) = 100(7 - 3) + 500 = 100(4) + 500 = 400 + 500 = 900
\]

5. **For \( t = 8 \)**:
\[
M(8) = 100(8 - 3) + 500 = 100(5) + 500 = 500 + 500 = 1000
\]

### Filled Table
Now we can compile the results into a table format:

| \( t \) (hours) | \( M(t) \) (cost in dollars) |
|------------------|-------------------------------|
| 4 | 600 |
| 5 | 700 |
| 6 | 800 |
| 7 | 900 |
| 8 | 1000 |

This table summarizes the cost based on the additional hours required beyond the initial 3 hours.