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To solve this problem, we need to calculate how the temperature changes over time based on the given rates of temperature change when the freezer is unplugged and when it is plugged back in.

### Breakdown:
1. The freezer starts at \(-14^\circ C\).
2. It warms up by \(3^\circ C\) per hour.
3. When the temperature rises above \(0^\circ C\), it is plugged back in, and the temperature begins to decrease by \(4^\circ C\) per hour.

### Step-by-step solution:
#### 1. Warming Phase (Unplugged):
- **Initial temperature:** \(-14^\circ C\).
- It warms by \(3^\circ C\) each hour.

- Hour 1: \(-14^\circ C + 3^\circ C = -11^\circ C\).
- Hour 2: \(-11^\circ C + 3^\circ C = -8^\circ C\).
- Hour 3: \(-8^\circ C + 3^\circ C = -5^\circ C\).
- Hour 4: \(-5^\circ C + 3^\circ C = -2^\circ C\).
- Hour 5: \(-2^\circ C + 3^\circ C = +1^\circ C\).

At the end of the 5th hour, the temperature reaches \(+1^\circ C\), which is above \(0^\circ C\), so the freezer is plugged back in.

#### 2. Cooling Phase (Plugged in):
- After it is plugged back in at \(+1^\circ C\), it cools by \(4^\circ C\) per hour.

- Hour 6: \(+1^\circ C - 4^\circ C = -3^\circ C\).
- Hour 7: \(-3^\circ C - 4^\circ C = -7^\circ C\).
- Hour 8: \(-7^\circ C - 4^\circ C = -11^\circ C\).

### Final Answer:
After 8 hours, the temperature of the freezer is \(-11^\circ C\).

Let me know if you'd like further details or if you have any questions.

### Related Questions:
1. What would the temperature be after 10 hours?
2. How long would it take for the freezer to reach \(-20^\circ C\) after being plugged in?
3. How would the problem change if the freezer warmed at \(2^\circ C\) per hour instead?
4. At what hour would the freezer first reach \(0^\circ C\)?
5. What would happen if the freezer was plugged in when it reached \(-5^\circ C\)?

### Tip:
Always break the problem down into phases (e.g., warming and cooling) to make the calculations more organized!

A freezer is at -14°C and then it is unplugged. It gets warmer by 3°C an hour. It is checked once an hour and when it gets above 0°C, it is plugged back in. After it is plugged in again, it gets colder by 4°C per hour. What is the temperature of the freezer (in °C) 8 hours after it was unplugged?

Learn how to calculate the temperature of a freezer after 8 hours of linear temperature changes. It starts at -14°C, warms by 3°C per hour, and cools by 4°C per hour after being plugged back in. This detailed solution includes calculations and step-by-step breakdowns, suitable for students in Grades 6-8.

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