Can you give a half-life for an exponentially decaying quantity?

Question

The half-life of a drug in the bloodstream is 4 hours. By what factor does the concentration of the drug decrease in 24 hours? in 36 hours?

Answer 1

1/2=e^-4k
-ln2=-4k
k=ln 2 /4=0.1732868
C/Co=e^-.1732868t
24 hrs C/Co=.015625
36 hours C/Co=0.001953125

You could do the by saying that 24*4*6 so after 24 hrs
C/Co=.5^6=.015625
& 36=4*9 so after 36 hrs
C/Co=.5^9=.001953125
Much easier but only works for t=4n where N is an integer

Answer 2

F = 1 / ( 2^(t/4) )

Answer 3

24 hours = 6 half lives = 2^(-6) = 1/64
36 hours = 9 half lives = 2^(-9) = 1/512

now multiply it by original drug concetration and compare to drug test threshold.