Answer
Amount after 1000 years = 4.43g. Amount after 10,000 years = 1.49g.
Work Step by Step
First, solve for the rate constant, k, then solve for the amount after 1000 years and 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
$\frac{1}{2}=e^{k(5715)}$
$\ln\frac{1}{2}=k5715$
$k=\frac{\ln\frac{1}{2}}{5715}$
$k\approx-1.2129\times10^{-4}$
Solve for amount after 1000 years using t = 1000.
$y=5e^{k1000}$
$y\approx4.43$
Solve for the amount after 10,000 years using t = 10000.
$y=5e^{k10000}$
$y\approx1.49$
