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.
\(200\times(\frac12)^{4.97131931}\)
\(200\times0.0318774644\)
\(\boxed{6.37549288\ grams}\)
