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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Darrell

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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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