Question 1025723: A pharmaceutical company is developing a new drug. The level of the new drug reduces by 28% each hour after it is taken by the patient. It is recommended that one tablet is taken initially and a second tablet is taken when the level of the drug in the first tablet has reduced by half. The pharmaceutical company would like to put a recommendation on the packet about how often one tablet should be taken. Investigate the time it takes for the level of this drug to reduce by half and make a recommendation to the company about how often one tablet should be taken.
Found 2 solutions by FrankM, Theo:
Answer by FrankM(1040)   (Show Source):
You can put this solution on YOUR website! 28% reduction is the same as multiplying by .72 , note that 1-.28=.72
.72^2 or .72*.72 = .5184 so 2 hours.
if we waited till the 3rd hour, there would be .373 or 37% well below the 50% level.
Last, the exact way to calculate a more complex problem is
.72^N=.5
So if we believe the body metabolizes to this level of accuracy, the precise answer is 2 hours 6 minutes 36 seconds. Each teacher will have their own requirements for levels of accuracy. It's absurd to see a number like 28% with 2 digits of accuracy, but then produce my answer down to the second, about 5 digits of accuracy. I offer it only to show the precise calculation.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the drug reduces by 28% each hour.
level of the drug after 1 hour is therefore 1 - .28 * 1 = .72
you want to find when the drug reaches .5
formula to use would be .5 = .72 ^ n
n equals the number of hours.
take the log of both sides of this equation to get log(.5) = log(.72^n).
since log(.72^n) is equal to n * log(.72), the equation becomes log(.5) = n * log(.72).
divide both sides of this equation by log(.72) to get n = log(.5) / log(.72).
this results in n = 2.110010956 hours.
since 2.11 hours is close to 2 hours, you would probably recommend the pill be taken every 2 hours.
in 2 hours, the level of the pill would be .72^2 = 51.84% of its original strength.
that's pretty close and much easier to remember than 2 hours and 6 or 7 minutes.
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