Question

In 1978, a 200-gram sample of cobalt-60 was buried in the Yucca Mountains, just northwest of Las Vegas, Nevada. How much of this sample was present in 2004? The half-life of cobalt-60 is 5.23 years.

Answer 1

1978 to 2004 is 26 years.
Every 5.23 years, half of our 200-gram sample decays.
It has reached its half life ~4.97 times.
We use this formula to find our new amount:

$200\times(\frac12)^\frac{26}{5.23}$

Every time it reaches its half life, it will be halved...the fractional exponent there is to pick up minute differences like in our 4.97.

$200\times(\frac12)^{4.97131931}$

$200\times0.0318774644$

$\boxed{6.37549288\ grams}$