SOLUTION: Hello, I was wondering if there is anyone that could help me with this problem. Any help at all would be greatly appreciated. THanks A drug is eliminated from the body through

Question 117581This question is from textbook Fundamentals of Alg and Trig
: Hello, I was wondering if there is anyone that could help me with this problem. Any help at all would be greatly appreciated.
THanks
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 llife of the drug? This question is from textbook Fundamentals of Alg and Trig

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
Let A(t) = 2 and solve for "t":
2 = 10(0.8)^t
0.2 = (0.8)^t
Take the log of both sides to get:
log0.2 = tlog(0.8)
t = [log0.2/log0.8]
t = 7.2126 hrs
-----------------------
b)WHat is the half life of the drug?
Let A(t) = (1/2)A(0) and solve for "t":
(1/2)(A(0)) = A(o)(0.8)^t
0.5 = (0.8)^t
Take the log:
t = [log0.5]/[log0.8] = 3.1063 hrs
===============
Cheers,
Stan H.

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