Homework Help: Logarithmic Half-Life prob.

SETHOSCOTT · May 6, 2009

1. The problem statement, all variables and given/known data
The half-life of a radioactive substance is 194 days. How many days will it take for 80% of the substance to decay?

2. Relevant equations

3. 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.

diazona · May 6, 2009

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 · May 6, 2009

In one "half life", T, (1/2)C= Ce^kT. The Cs cancel, and you solve that for k. After you know that you can solve 0.8C= Ce^kt for t.

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

diazona · May 6, 2009

SETHOSCOTT said: ↑

3. 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...

SETHOSCOTT · May 6, 2009

=) omg! Thanks!

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Homework Help: Logarithmic Half-Life prob.

SETHOSCOTT

diazona

HallsofIvy

diazona

SETHOSCOTT