Answer
Initial amount = 7.63g. Amount after 1000 years = 4.95g.
Work Step by Step
First, solve for the rate constant, k, then solve for initial amount. Lastly solve for quantity after 1000 years.
Decay formula:
$y=Ce^{kt}$
Understanding that half-life means half of the product has degraded after set amount of time, t = 1599
$\frac{1}{2}=e^{k(1599)}$
$\ln\frac{1}{2}=k1599$
$k=\frac{\ln\frac{1}{2}}{1599}$
$k\approx-4.3349\times10^{-4}$
Solve for initial amount using given amount after 10000 years.
$0.1 = Ce^{k(10000)}$
$0.1 = Ce^{(-4.3349\times10^{-4})(10000)}$
$C\approx7.63$
Solve for amount after 1000 using t = 1000.
$y=7.63e^{k(1000)}$
$y\approx4.95$
