# Pre Calc!

A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by A(t)=10(0.8)^t and that in order for the drug to be effective, at least 2 milligrams must be in the body.

(a) Determine when 2 milligrams is left in the body.

(b) What is the half-life of the drug?

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1. a)
A(t)=A0(0.8)^t
For 2 mg left, we have A(t)=2, A0=10, so
2=10(0.8)^t
0.8^t = 1/5
take ln on both sides,
t*ln(0.8)=ln(1/5)
t=ln(0.2)/ln(0.8)
=7.2 hours

b)
Half-life is the time it takes to reduce the quantity to 0.5A0, i.e.
5=10(0.8)^t
solve for t similar to a) above.

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2. Thank you!

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3. You're welcome!

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