Question

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How many milligrams of caffeine will be in your system after 8 hours? Round to two decimal places? Can someone show me how to work this problem out?

Answer 1

43.16 mg

Explanation:

After each hour, the amount remaining is 100% - 12% = 0.88 times the amount present at the beginning of the hour. Then after 8 hours, the amount remaining will be the initial amount multiplied by 0.88 eight times, or ...

(120 mg)·(0.88^8) ≈ 43.1561 mg ≈ 43.16 mg

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Of course, an exponent is used to signify repeated multiplication. You can actually do the multiplication if you like, but most scientific and graphing calculators handle exponentiation easily.