Answer
Initial amount = 2.31g. Amount after 10,000 years = 0.03g.
Work Step by Step
First, solve for the rate constant, k, then solve for initial amount. Lastly solve for quantity 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 = 1599
$\frac{1}{2}=e^{k(1599)}$
$\ln\frac{1}{2}=k1599$
$k=\frac{\ln\frac{1}{2}}{1599}$
$k\approx-4.33\times10^{-4}$
Solve for initial amount using given amount after 1000 years.
$1.5 = Ce^{k(1000)}$
$1.5 = Ce^{(-4.33\times10^{-4})(1000)}$
$C\approx2.31$
Solve for amount after 10,000 using t = 10,000.
$y=2.31e^{k(10,000)}$
$y\approx0.028\approx0.03$
