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:
[tex]200\times(\frac12)^\frac{26}{5.23}[/tex]
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.
[tex]200\times(\frac12)^{4.97131931}[/tex]
[tex]200\times0.0318774644[/tex]
[tex]\boxed{6.37549288\ grams}[/tex]
