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!