Let's solve the problem step-by-step and interpret the function \( M(t) = 9t + 25 \):
1. Define the Components:
- The base fee Hazel charges is \( \$25 \).
- Additionally, she charges \( \$9 \) for every hour she mows.
2. Understand the Linear Function:
- \( M(t) \) represents the total amount of money Hazel earns for mowing for \( t \) hours.
- The function is given by \( M(t) = 9t + 25 \).
3. Substitute \( t = 2 \) into the Function:
- We are asked to find \( M(2) \), which means we need to substitute 2 for \( t \) in the function.
- So, \( M(2) = 9(2) + 25 \).
4. Calculate the Expression:
- First, calculate \( 9 \times 2 \):
[tex]\[
9 \times 2 = 18
\][/tex]
- Next, add the base fee of \( \$25 \):
[tex]\[
18 + 25 = 43
\][/tex]
5. Interpret the Result:
- Thus, \( M(2) = 43 \).
- The interpretation of this result is that if Hazel mows a yard for 2 hours, she will earn \( \$43 \).
So, the correct interpretation is:
[tex]\[ M(2) = 43; \text{ If Hazel mows a yard for 2 hours, she will earn } \$43. \][/tex]
