You work in a materials testing lab and your boss tells you to increase the temperature of a sample by `40.0^@ C`. The only thermometer you can find at your workbench reads in `^@ C`. If the initial temperature of the sample is `68.2^@ C`. What is its temperature in `^@ C` when the desired temperature increase has been achieved ?

Explanation

To solve the problem of finding the final temperature after increasing the initial temperature by a certain amount, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Temperature (T1)**:
The initial temperature of the sample is given as \( T_1 = 68.2^\circ C \).

2. **Determine the Temperature Increase (ΔT)**:
The desired increase in temperature is given as \( \Delta T = 40.0^\circ C \).

3. **Calculate the Final Temperature (T2)**:
The final temperature can be calculated using the formula:
\[ T_2 = T_1 + \Delta T \]
Substituting the known values:
\[ T_2 = 68.2^\circ C + 40.0^\circ C \]

4. **Perform the Addition**:
\[ T_2 = 108.2^\circ C \]

5. **State the Final Result**:
The final temperature of the sample after the increase is \( T_2 = 108.2^\circ C \).

### Final Answer:
The temperature of the sample after the desired increase is **108.2°C**.

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