SOLUTION: Suppose the half-life of a drug is 16 hours. When will 94% of the drug be removed from the body? Use the equation: Q(t)=q0e^-kt

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Suppose the half-life of a drug is 16 hours. When will 94% of the drug be removed from the body? Use the equation: Q(t)=q0e^-kt      Log On


   

Question 1116554: Suppose the half-life of a drug is 16 hours. When will 94% of the drug be removed from the body? Use the equation: Q(t)=q0e^-kt
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
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... Use the equation: Q(t)=q0e^-kt.
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Q%28t%29=q%5Bo%5De%5E%28-kt%29
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If that is the way you want to make the model, then for the half-life information,

1%2F2=e%5E%28-kt%29
ln%28e%5E%28-kt%29%29=ln%281%2F2%29
-kt=ln%281%2F2%29, and t=16;
k=ln%281%2F2%29%2F%28-16%29
k=ln%282%29%2F16
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k=0.04332 and more specific model equation is Q%28t%29=q%5Bo%5De%5E%28-0.04332t%29.

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When will 94% of the drug be removed from the body?
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That's same as 6% remaining in the body.
100%2Ae%5E%28-0.04332%2At%29=6
e%5E%28-0.04332t%29=0.06
-0.04332t=ln%280.06%29
t=ln%280.06%29%2F%28-0.04332%29
highlight%28t=65%29,hours