SOLUTION: The function f(x)= 40(0.8)^x gives the amount of a medication in milligrams present in a patient's system x hours after taking a 40-mg dose. In how many hours will there be less th

Algebra ->  Functions -> SOLUTION: The function f(x)= 40(0.8)^x gives the amount of a medication in milligrams present in a patient's system x hours after taking a 40-mg dose. In how many hours will there be less th      Log On


   

Question 447792: The function f(x)= 40(0.8)^x gives the amount of a medication in milligrams present in a patient's system x hours after taking a 40-mg dose. In how many hours will there be less than 2 mg of the drug in a patient's system?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The function f(x)= 40(0.8)^x gives the amount of a medication in milligrams present in a patient's system x hours after taking a 40-mg dose. In how many hours will there be less than 2 mg of the drug in a patient's system?
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set f(x) to 2 and solve for x:
2+=+40%280.8%29%5Ex
2%2F40+=+%280.8%29%5Ex
take log base .8 of both sides:
log%280.8%2C2%2F40%29+=+x
change of base:
log%282%2F40%29%2Flog%280.8%29+=+x
13.43+=+x
answer:
more than 13.43 hours