Answered

A certain tranquilizer decays exponentially in the bloodstream and has a ​half-life of 47 hours. How long with it take for the drug to decay to 82​% of the original​ dose?
This is a​ two-step problem.

Sagot :

The drug will decay to 82% of the initial dosage after 7.18 hours.

Finding the Decay constant(λ):

λ = 0.693 / (half-life)

we are given that the half-life is 47 hours

λ = 0.693 / (47)

λ = 0.01925 /hour

Time is taken for 82% decay:

How do find the decay?

Since decay is first-order, we will use the formula:

[tex]t = \frac{2.303}{0.0192} log\frac{100}{82}[/tex]

Final amount = 100*82/100 = 82 mg

Replacing the values in the equation:

t = 2.303/ 0.0192 x 0.06

t = 7.18 hours

Therefore, the drug will decay to 82% of the initial dosage after 7.18 hours.

Learn more about half-life;

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