Question

A drug used to relieve anxiety and nervousness has a half-life of 16 hours. if a doctor prescribes one 2.8-milligram every 24 hours, then what percentage of the last dosage remains in the patient’s body when the next dosage is taken

Answer 1

After 24 hours, 35.4% of the initial dosage remains on the body.

What percentage of the last dosage remains?

The exponential decay is written as:

$f(x) = A*e^{-k*x}$

Where A is the initial value, in this case 2.8mg.

k is the constant of decay, given by the logarithm of 2 over the half life, in this case, is:

$k = ln(2)/16h$

Replacing all that in the above formula, and evaluating in x = 24 hours we get:

$f(24h) = 2.8mg*e^{-24h*ln(2)/16h} = 0.9899 mg$

The percentage of the initial dosage that remains is:

$P = \frac{0.9899mg}{2.8mg}*100\% = 35.4\%$

If you want to learn more about exponential decays:

brainly.com/question/11464095

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