Posted by **Hayli** on Tuesday, September 14, 2010 at 7:17pm.

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?

- Pre Calc! -
**MathMate**, Tuesday, September 14, 2010 at 7:28pm
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.

- Pre Calc! -
**Hayli**, Tuesday, September 14, 2010 at 7:46pm
Thank you!

- Pre Calc! -
**MathMate**, Tuesday, September 14, 2010 at 8:08pm
You're welcome!

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