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Suppose you are trying to determine the shelf-life of a new pharmaceutical to be able to...

Suppose you are trying to determine the shelf-life of a new pharmaceutical to be able to estimate the expiration date. You test a batch of pills over a period of time. The pills start with 500 mg active ingredient. A table of the results is given below:

(Months, mg of chemical remaining): (0, 500) (3, 465) (6, 395) (9, 378) (12, 320) (15, 310) (18, 284)

Given that the many pharmaceutical are considered “expired” when they lose 10% of their potency, what is the most accurate estimate of the expiration time for your chemical (in units of months)?

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Answer:

It's given that the medicine is considered expired when they loose 10% of their potency.

Amount of chemical at 0 time - 500 mg

10% of 500=50 mg

Therefore the most appropriate time of expiry would be when the chemical content is below 450.

After 3 months, there is still 15 mg chemicals more than 10% potency. But after 6 months it is totally expired.  

So if we have to choose between these options then most accurate would be 3 months.

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