# Logarithmic Half-Life prob.

## Homework Statement

The half-life of a radioactive substance is 194 days. How many days will it take for 80% of the substance to decay?

## The Attempt at a Solution

I had to make 1/2n=1/5. I did this by finding log25=n. After this, I needed to only multiply by the number of days it took the half-life to occur, which was 194, and got 451 (approx.) as a reasonable answer.

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diazona
Homework Helper
There is absolutely enough information there. I could tell you the answer right now (but I won't, that's what you get to do ;-)

I'd advise you to go back and double-check that equation, though.

HallsofIvy
Homework Helper
In one "half life", T, (1/2)C= CekT. The Cs cancel, and you solve that for k. After you know that you can solve 0.8C= Cekt for t.

But you don't need to use "e". If T is the half life then $C(t)= C(0)(1/2)^{t/T}$ because every time "T" days, you multiply by1/2. Solve $.8C= C(1/2)^{t/194}$.

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diazona
Homework Helper

## The Attempt at a Solution

I had to make 1/2n=1/5. I did this by finding log25=n. After this, I needed to only multiply by the number of days it took the half-life to occur, which was 194, and got 451 (approx.) as a reasonable answer.
Looks good...

=) omg! Thanks!