Question

For the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17% each hour.

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 24 hours. Round to the nearest hundredth of a gram. 

Answer 1

Consider that a doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17% each hour.

Suppose that amount of the drug remaining after t hours is,

f(t) = 300crt

So,

0.83(300) = 300er(t)

             er = 0.83

               r = ln(0.83)

               r = -0.186

 

So, the amount of the drug remaining after t hours is,

    f(t) = 300e-0.186t

Put, t = 24

So,

f(24) = 300e-0.186(24)

         = 300(0.011516)

         = 3.45

 

Hence, the amount of drugs remaining after 24 hours is 3.45 milligrams.

Hence, the amount of drugs remaining after 24 hours is 3.45 milligrams.