Answer
Initial quantity = 1.82g. Amount after 10,000 years = 0.54g.
Work Step by Step
First solve for rate constant, k, then solve for initial quantity using amount left after 1000 years. Lastly solve for amount left after 10,000 years.
Decay formula:
$y=Ce^{kt}$
Understanding that half-life means half of the product has degraded after set amount of time, t = 5715
$\frac{1}{2}=e^{k(5715)}$
$\ln\frac{1}{2}=k5715$
$k=\frac{\ln\frac{1}{2}}{5715}$
$k\approx−1.2129×10^{−4}$
Solve for initial amount using amount left after 1000 years.
$1.6=Ce^{k(1000)}$
$C\approx1.82$
Solve for amount after 10,000 using t = 10000.
$y=1.81e^{k(10000)}$
$y\approx0.54$
