Advanced MathMediumChoosing a decay model
Advanced Math practice question
A cup of coffee is 40 degrees above room temperature, and the difference decreases by 15% every 5 minutes. Which function gives the temperature difference D after t minutes?
- A. D(t) = 40(0.85)^(t/5)Correct
- B. D(t) = 40(0.15)^(t/5)
- C. D(t) = 40(0.85)ᵗ
- D. D(t) = 40 − 6t
Answer: A. D(t) = 40(0.85)^(t/5)
Each 5-minute period keeps 85%: exponent t/5 counts the periods.
Why the other answers are wrong
- B. D(t) = 40(0.15)^(t/5)
- 0.15 keeps 15%, an 85% decrease.
- C. D(t) = 40(0.85)ᵗ
- An exponent of t applies the 15% drop every minute instead of every 5 minutes.
- D. D(t) = 40 − 6t
- 40 − 6t is linear, subtracting 15% of the original each period.
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