Question
A pan from the oven is sitting out to cool to room temperature. If the temperature difference between the pan and room temperature is currently 174°C and is decreasing by 5% every minute, how much above room temperature will the pan be in 21 minutes?
If necessary, round your answer to the nearest tenth.
If necessary, round your answer to the nearest tenth.
Answers
GPT 3.5
The temperature difference is decreasing by 5% every minute, so the new temperature difference after 1 minute is 0.95 * 174°C = <<0.95*174=165.3>>165.3°C.
After 2 minutes, the temperature difference is 0.95 * 165.3°C = <<0.95*165.3=157.1>>157.1°C.
In 21 minutes, the temperature difference will be 0.95^21 * 174°C = <<0.95^21*174=83.3>>83.3°C above room temperature.
So the pan will be 83.3°C above room temperature. Answer: \boxed{83.3}.
After 2 minutes, the temperature difference is 0.95 * 165.3°C = <<0.95*165.3=157.1>>157.1°C.
In 21 minutes, the temperature difference will be 0.95^21 * 174°C = <<0.95^21*174=83.3>>83.3°C above room temperature.
So the pan will be 83.3°C above room temperature. Answer: \boxed{83.3}.