1 answer

A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. Exponential modelling problem?

Question:

a) To the nearest hour, what is the half-life of the drug?
I have the general form of an exponential function, I'm not sure how to use this to solve for the half life though.

b) Write an exponential model representing the
amount of the drug remaining in the patient’s
system after t hours. Then use the formula to find
the amount of the drug that would remain in the
patient’s system after 3 hours. Round to the nearest
milligram.


Answers

Exponential decay model: #y=x(1-r)^t# , half life of tablet is about #2# hours and after #t=3# hours , remaining drug on patient's system is #42.875# mg.

Explanation:

Initial drug #x=125# mg ; rate of decay #r=30/100=0.3# gm/hour

Exponential model: #y=x(1-r)^t=125(1-0.3)^t=125*0.7^t#

Half life: # y=125/2=62.5#mg # :. 62.5 = 125*0.7^t# or

#0.7^t= 1/2 # . Taking logarithm on both sides we get ,

#t log (0.7) = log (0.5) :. t= log(0.5)/log(0.7)~~1.94(2dp)# hour

The half life of tablet is about #2# hours.

After #t=3# hours , remaining drug on patient's system is

#y=125*0.7^t=125*0.7^3=42.875# mg [Ans]

.

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