A patient is given a 50 mg dose of medicine. The medicine's effectiveness decreases every hour at a constant rate of 40%. What is the exponential decay function that models this scenario? How much medicine will be left in the patient's system after 2 hours?
It should be noted that only 60% of the medicine of the previous hour is left n the patient's system every hour. Thus, the model of the scenario is,
D = 50 mg (0.6^n)
where D is the dosage at any hour n.
Using the model above with n equal to 2. D becomes 18. Therefore, only 18 mg is left in the patient's system after 2 hours.
The quantity of the medicine left in the patient's system after 2 hours is 18 mg.
Consider the function:
\(y = a(1\pm r)^m\)
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
It should be noted that only 60% of the medicine of the previous hour is left n the patient's system every hour.
Thus, the model of the scenario,
\(D = 50 ( 1 - 0.4)^n\\\\D = 50 (0.6^n)\)
where D is the dosage at any hour n.
From the model above with n equal to 2 then D becomes 18.
Hence, The quantity of the medicine left in the patient's system after 2 hours is 18 mg.
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