7
advanced-math

The temperature of coffee cools from 90°C to 45°C in 10 minutes. If it cools exponentially, what is the decay factor per 10 minutes?

A

0.5

B

2

C

45

D

0.9

Correct Answer: A

Choice A is the correct answer. Calculate the ratio after one time period.

  1. Initial: T0=90°CT_0 = 90°C.
  2. After 10 min: T=45°CT = 45°C.
  3. Decay Factor: b=4590=0.5b = \frac{45}{90} = 0.5.

💡 Strategic Tip: Decay factor = finalinitial\frac{\text{final}}{\text{initial}} over one time period.

Choice B is incorrect because this would be growth, not decay. Choice C is incorrect because this is the temperature, not the factor. Choice D is incorrect because this doesn't match the ratio.

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Set 28: Exponential Functions 28