Calculating with Half Lives

1. Apr 25, 2007

sin_city_stunner

1. The problem statement, all variables and given/known data

1. A radioisotope has a half-life of 24 a and an initial mass of 0.084g. Approximately how many years will have passed if only 10% of the isotope remains?

2. Relevant equations

m= original mass * (1/2)^t t = # of half lives

3. The attempt at a solution

10% of the isotope = (.084 g)(0.1)
= 0.084 g

.0084g = .084g * (1/2)^t
0.1 g = (1/2)^t

It is there where i get stuck. I try to make bases the same so the exponents are equal to each other, but can't get it for some reason.

Thanks

2. Apr 25, 2007

hage567

Have you seen this before:

$$M=M_oe^{-\lambda t}$$

where $$\lambda= \frac{\ln(2)}{ T_{\frac{1}{2}}}$$

3. Apr 25, 2007

sin_city_stunner

we've just learned the second equation, but have never seen the first one one before

4. Apr 26, 2007

symbolipoint

Do you have that backwards?

5. Apr 26, 2007

symbolipoint

The first equation, $$M=M_oe^{-\lambda t}$$
is the usual equation for exponential decay.