Question

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 22 minutes?

Answer 1

The temperature after 22 minutes is 75.75 degrees

Equations and exspressions

Given the resulting exponential model for the temperature, t, after m minutes can be approximated by the model t = 133(0.85)^m + 72.

If the time used is 22 minutes, the required temperature dring this time is expressed as:

t = 133(0.85)^22 + 72

t = 3.725 + 72

t = 75.75

Hence the temperature after 22 minutes is 75.75 degrees

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