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Question

The​ half-life of a certain tranquilizer in the bloodstream is

32 hours. How long will it take for the drug to decay to 85​% of the original​ dosage? Use the exponential decay​ model, A=A0ekt​, to solve.

Answer 1

in 32 half or 50%is left. in 64 half of half or 1/4 or 25% is left, as 75% decayed

1/2 = e^32k

ln.5 = 32k

k = ln.5/32= about -0.022

1/4=e^-,022t

ln.25=-,022t

t=ln,25/-,022= about 64 years

.85=e^-.022t

ln.85=-.022t

t= ln.85/-,022= about 7.4 years

or if possibly you meant when does 85% decay

then use

.15= e^-.022t

where t = over 86.2 years