Question
8) A cup of 205° coffee on a table in a 72° room loses approximately 15% of its temperature every minute until it reaches room temperature. The resulting exponential model for the temperature, t, after m minutes can be approximated by the model t = 133(0.85)m + 72. What is the temperature after 9 minutes? Round your answer to the nearest whole degree.
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Answer to a math question 8) A cup of 205° coffee on a table in a 72° room loses approximately 15% of its temperature every minute until it reaches room temperature. The resulting exponential model for the temperature, t, after m minutes can be approximated by the model t = 133(0.85)m + 72. What is the temperature after 9 minutes? Round your answer to the nearest whole degree.
Darrell
4.597 Answers
1. Start with the given formula for the temperature:
t = 133(0.85)^m + 72
2. Substitute \( m = 9 \) into the equation:
t = 133(0.85)^9 + 72
3. Evaluate the exponential term:
(0.85)^9 \approx 0.24715
4. Multiply by 133:
133 \times 0.24715 \approx 32.89895
5. Add 72:
32.89895 + 72 \approx 104.89895
6. Round to the nearest whole degree:
t \approx 103 \text{ degrees Fahrenheit}
The temperature of the coffee after 9 minutes is approximately:
t \approx 103 \text{ degrees Fahrenheit}
2. Substitute \( m = 9 \) into the equation:
3. Evaluate the exponential term:
4. Multiply by 133:
5. Add 72:
6. Round to the nearest whole degree:
The temperature of the coffee after 9 minutes is approximately:
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