8

Set 11: Exponential Functions (Intermediate)

Explanation

Answer: A

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

✓ Correct
B.

2

C.

45

D.

0.9

Detailed Explanation

Choice A is correct. 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.

Key Steps:

The correct answer is 0.5

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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