Question

Researchers are recording how much of an experimental medication is in a person's bloodstream every hour. they discover that half-life of the medication is about 6 hours.​

Answer 1

By using the known half-life, we can see that if the initial dose is 500mg, after 4 days the medication will be 0.0076 mg.

What is the half-life?

We define half-life as the time such that the initial amount is reduced to its half.

So, if a given substance has a half-life T, then the amount of substance as a function of time, we have:

S(t) = A*e^{-t*ln(2)/T}

Where t is the variable in time units.

We know that T = 6 hours, and A, the initial dose, is 500 mg, so the formula is:

S(t) = 500mg*e^{-t*ln(2)/6h}

Then after 4 days (or 4*24h = 96h) the amount of medication is:

S(96h) =  500mg*e^{-96h*ln(2)/6h} = 0.0076 mg.

If the initial dose was 750mg, after 4 days the person would have:

S(96h) = 750mg*e^{-96h*ln(2)/6h} = 0.0114 mg

So the person would have:

0.0114 mg -  0.0076 mg = 0.038 mg more of medication.

If you want to learn more about the half-life, you can read:

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