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
4.5

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

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}

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