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)
- 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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