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Help with Logs!

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I am stuck on this problem and have tried a few times but seem to not be getting the right answer.  I am thinking maybe I need to do a ln, but the answer I have gotten have been a little wacky.  Could you please help me?

1) The formula A=6e-0.38t  can be used to determine the number of milligrams, A, of a certain drug in a patient’s bloodstream t  hours after the drug has been administered.

2) When the number of milligrams of the drug reaches 3.1, the drug is to be administered again.  How many hours will elapse between injections?

Feb 22, 2019

1+0 Answers

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We have that

6e^(-0.38t) = 3.1       divide both sides by 6

e^(-0.38t)  =  3.1 /  6       take the Ln of both sides

Ln e^(-0.38t) = Ln ( 3.1 / 6 )

Using a log property, we can write

(-0.38t) Ln e  = Ln ( 3.1 / 6)

Since Ln e = 1, we can ignore this....and we have

-0.38t  = Ln ( 3.1 / 6)      divide both sides by -0.38

t =  Ln (3.1 / 6) / ( -0.38)  ≈  1.73 hrs between injections

Feb 22, 2019