# 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.