How Long Until Only 10% of a Radioisotope Remains?

[sin_city_stunner]

Homework Statement

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?

Homework Equations

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

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

 

[hage567]

Have you seen this before:

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

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

 

[sin_city_stunner]

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

 

[symbolipoint]

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

Do you have that backwards?

 

[symbolipoint]

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