The half life of a cortain tranquilizer in the bloodstream i

The half life of a cortain tranquilizer in the bloodstream is 48 hours. How long will i take for the drug to decay to 88% ofthe original dosage? Use the exponential decay model, A=A0 ekt, to solve. hours Round to one decimal place as needed.) er you Enter your answer in the answer box and then click Check Answer parts remain All parts showing Cleer A 7

Solution

A=A₀e^kt

(A₀/2)=A₀e^48k

ln(1/2) =48k

k=(1/48)ln(1/2)

A=A₀e^{t(1/48)ln(1/2)}=A₀(1/2)^t/48

0.88=(1/2)^t/48

log(0.88) = (t/48) log 0.5

t=8.9 hours