Caffeine withdrawal

Another familiar drug, caffeine, decreases in your body by 12% per hour. If you’re planning to drink a cup before a long exam it might be very useful to know how long it takes for the caffeine to diminish before you to need more to stay alert.

If you start with a standard cup of coffee containing 120mg of caffeine, how long before the effects wear off? (Note: You might be affected by as little as 50 mg)

(To make this problem interactive, turn on javascript!)

I need a hint: 100% - 12% = 88%
... another hint ... : 120×0.88^?? To what exponent would you need to raise 0.88 for caffeine levels to to fall below 50 mg?
... still more... : need to do some “plug-and-chug” here (in other words, make some guesses) ...
... some guesses... : 120×0.88¹ = 105.6 mg
... some guesses... : 120×0.88² = 92.9 mg
... some guesses... : 120×0.88³ = 81.8 mg
... your turn ... : keep hitting "x 0.88" on your calculator, you'll get there eventually

I think I have the answer: 120×0.88⁷ = 49mg, so about 7 hours.

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MathBench > Population Dynamics

Exponential Growth and Decay

Table of Contents

Caffeine withdrawal

If you start with a standard cup of coffee containing 120mg of caffeine, how long before the effects wear off? (Note: You might be affected by as little as 50 mg)

I think I have the answer: 120×0.88⁷ = 49mg, so about 7 hours.

MathBench > Population Dynamics

Exponential Growth and Decay

Table of Contents

Caffeine withdrawal

If you start with a standard cup of coffee containing 120mg of caffeine, how long before the effects wear off? (Note: You might be affected by as little as 50 mg)

I think I have the answer: 120×0.887 = 49mg, so about 7 hours.

I think I have the answer: 120×0.88⁷ = 49mg, so about 7 hours.