Question

The function f(x) = 40(.8)x gives the amount of a medication in milligrams present in a patient’s system x hours after taking a 40mg dose. A patient can go back to work if he or she has less than 1 mg left in his system. The patient takes the medication at 8pm on Monday night. Explain when he can go back to work. Justify your answer by showing all the work.

Answer 1

f(x) = 40(0.8^x)
So now just solve
40(0.8^x) = 1
0.8^x = 1/40
x = -log40/log0.8
That will be the number of hours. Just change that to clock time.