So what can you do with exponential growth and shrinkage models? Turns out, an awful lot. The following pages contain issues from ecology, environment, economics, medicine ... Remember that ANYTIME a population or collection of things changes by a constant PERCENTAGE, that’s exponential. Have fun!
Over the counter pain medications – like ibuprofen (the main ingredient in a leading brand I don’t care to name) usually have dosing instructions on the bottle that say something like “take one or two tablets every 6 hours”. So you take the pills, and pain goes away, but pain starts coming back gradually before the 6 hours are up, increasing until you can take another dose. Turns out, you’re metabolizing the ibuprofen and the concentration is declining exponentially.
Ibuprofen metabolizes at approximately 29% each hour. If you start out with a 500mg dose, what will the concentration in your body be after 6 hours?
- I need a hint: We’re dealing with shrinkage here. What's the multiplier?
- ... another hint ... : The multiplier is 100% - 29% = 71% = 0.71.
- ... another hint ... : The exponent is the number of hours...
I think I have the answer: 500×0.716 = 64mg
What is the concentration in your body after 3˝ hours (when you started to feel pain again)?
- I need a hint: Still using the same multiplier
- ... another hint ...: What should the exponent be?
I think I have the answer: 500×0.713.5 = 151mg
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