You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
half-life problem
- Thread starter desirae24
- Start date
I am trying to solve: What is the half life of a substance if 2.4 g decays to .8g in 64 hours?
I know how to solve a problem if I know the half-life but I can't figure out the equation if not. I know it has decayed .667.
.8=2.4(1/2)^64/t
Good work on the problem set-up.
First, divide both sides of the equation by 2.4. .8/2.4 = 1/3, so…
1/3 = (1/2)^64/t
Next take the log of both sides.
Log(1/3) = log((1/2)^64/t)
Now move the exponent to the coefficient position.
Log(1/3) = (64/t )(log(1/2))
Continue.
desirae24 said:\(\displaystyle > >\).8=2.4(1/2)^64/t\(\displaystyle < <\)
wjm11 said:\(\displaystyle > >\)1/3 = (1/2)^64/t\(\displaystyle < <\)
Next take the log of both sides.
\(\displaystyle > >\)Log(1/3) = log((1/2)^64/t)\(\displaystyle < <\)
Now move the exponent to the coefficient position.
Log(1/3) = (64/t )(log(1/2))
When anyone types this, it is to have grouping symbols around the exponent, 64/t,
because of the Order of Operations:
.8 = 2.4(1/2)^(64/t) and
1/3 = (1/2)^(64/t) and
log(1/3) = log[(1/2)^(64/t)]
Otherwise, for instance, the first equation highlighted by arrows is equivalent to:
\(\displaystyle .8 \ = \ \frac{ 2.4(1/2)^{64}}{t}.\)