Question

11. 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.

(4 points)
Function Cost of Moving Interpretation
M (4) $

M(8) $

Answer 1

To complete the table using the given function \( M(t) = 100(t - 3) + 500 \) for \( t > 3 \), we will calculate the cost of moving for \( t = 4 \) and \( t = 8 \).

1. **Calculate \( M(4) \)**:
\[
M(4) = 100(4 - 3) + 500
\]
\[
M(4) = 100(1) + 500 = 100 + 500 = 600
\]

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

Now we can fill in the table:

| Function | Cost of Moving | Interpretation |
|-----------|----------------|--------------------------------------|
| M(4) | $600 | The cost of moving for 4 hours is $600. |
| M(8) | $1000 | The cost of moving for 8 hours is $1000. |