8
advanced-math

A cup of coffee cools according to T(m)=90(0.92)mT(m) = 90(0.92)^m, where TT is temperature in Celsius and mm is minutes. What does 0.92 represent?

A

The temperature decreases by 0.92°C per minute.

B

The temperature decreases by 8% per minute.

C

The temperature is 92% of the initial temperature after 1 minute.

D

Both B and C are correct.

Correct Answer: D

Choice D is the correct answer. Both interpretations of the decay factor are valid.

  1. Analyze Factor: b=0.92b = 0.92 means each minute, the temperature becomes 92% of the previous minute's value (Choice C).
  2. Find Rate: r=1−b=1−0.92=0.08=8%r = 1 - b = 1 - 0.92 = 0.08 = 8\%. This means it decreases by 8% per minute (Choice B).
  3. Conclusion: Since both B and C are correct descriptions, D is the answer.

💡 Strategic Tip: A decay factor of 0.X0.X means retaining X0%X0\% and losing (100−X0)%(100-X0)\%.

Choice A is incorrect because exponential decay is percentage-based, not linear subtraction.

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Set 21: Exponential Functions 21