36
QuizMultiple Choice

N/A — Exam

Question 36 • Algebraic Reasoning

A cup of coffee contains 130 mg of caffeine. If caffeine is eliminated from the body at a rate of 11 percent per hour, how much caffeine will remain in the body after 3 hours? Write the exponential function and solve.

Answer
A
y is equal to 130 times 0 point 8 9 cubed ; 184 mg
B
y is equal to 130 times 0 point 8 9 cubed ; about 92 mg
C
y is equal to 130 times 3 to the 89th power ; about 346 mg
D
y is equal to 130 times 0 point 1 1 cubed ; less than 1 mg

Explanation

An 11% hourly elimination rate means 89% remains each hour, so the hourly multiplier is 0.89. The exponential function is y = 130(0.89)^t, where t is the time in hours. After 3 hours, y = 130(0.89)^3 ≈ 91.7 mg, or about 92 mg; this matches choice B.

AI-written and checked against the verified answer.

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