Question

For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour.

Using the model found in the previous exercise, find f(10) and interpret the result. Round to the nearest hundredth.

Answer 1

Consider that a doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour.

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

f(t) = 125ert

 

Therefore,

0.7(125) = 125er(1)

           er = 0.7

             r = ln(0.7)

             r = -36

 

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

   f(t) = 125t-0.36t

Put t = 10

 

Hence,

f(10) = 125{e-0.36(10)}

         = 125(0.027324)

         = 3.42

 

Hence, the amount of drugs remaining after 10 hours is 3.42 milligrams.

Hence, the amount of drugs remaining after 10 hours is 3.42 milligrams.