Advanced MathEasy–MediumChoosing the exponential model
Advanced Math practice question
A cup of coffee contains 200 milligrams of caffeine. The amount in the body falls by half every 5 hours. Which function gives the amount A, in milligrams, after t hours?
- A. A(t) = 200(1/2)^(t/5)Correct
- B. A(t) = 200(1/2)ᵗ
- C. A(t) = 200 − 20t
- D. A(t) = 200(5)^(t/2)
Answer: A. A(t) = 200(1/2)^(t/5)
Each 5-hour period halves the amount: the exponent t/5 counts the periods.
Why the other answers are wrong
- B. A(t) = 200(1/2)ᵗ
- (1/2)ᵗ halves every hour instead of every 5 hours.
- C. A(t) = 200 − 20t
- 200 − 20t is linear, not halving.
- D. A(t) = 200(5)^(t/2)
- A base of 5 grows the amount.
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