Answer
Initial amount = 10.1g. Amount after 1000 = 9.95g.
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 = 5715
$\frac{1}{2}=e^{k(5715)}$
$\ln\frac{1}{2}=k5715$
$k=\frac{\ln\frac{1}{2}}{5715}$
$k\approx-1.2129\times10^{-4}$
Solve for initial amount using given amount after 10,000 years.
$3 = Ce^{k(10000)}$
$3 = Ce^{(-1.2129\times10^{-4})(10000)}$
$C\approx10.1$
Solve for amount after 1000 using t = 1000.
$y=10.1e^{k(1000)}$
$y\approx9.95$
