# Having a hard time with logorhythms and e function...

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Posted by Autumn on October 09, 2002 at 14:51:45:

Hi there! I have a problem I'm trying to solve, and I'm having a hard time with it.

The problem is: The concentration y of a drug in a person's system decreases according to the relationship: y = 2e^-.125t
where y is in appropriate units, and t is in hours. Find the amount of time that it will take for the concentration to be half of its original value.

How would you set this problem up? To me, it seems there are two variables, y and t. The book gives the answer 5.5 hours, and if I set it up as:
1=2e^-.125t
1/2=e^-.125t
in.5=-.125t
in.5/-.125=t
then I get the answer 5.5

I don't understand why this works to use 1 for y...I thought to find 1/2 the concentration, I would need to use .5y and if I assume y is=1, then the problem would look like: .5(1)=2e^-.125t
.5=2e^-.125t
and so on, which gives me a wrong answer. I would like to understand how this works. Sorry if this is confusing...if it is, it's because I'm confused! Thanks!

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