Question 969137
{{{y=pe^(-kt)}}}
p, initial amount
y, final amount
k, a decay constant
t, time in years


k for the half-life:
{{{1/2=e^(-kt)}}}
{{{ln(1/2)=-kt}}}
{{{k=-ln(1/2)/t}}}
{{{k=ln(2)/t}}}
Given half life 5730 years.
{{{k=0.693147/5730=highlight(1.210*10^-4)}}}-------fixed earlier mistake.


What if y=20% of p?
{{{0.2=e^(-0.0001210*t)}}}
{{{ln(0.2)=-0.0001210*t}}}
{{{t=ln(0.2)/(-0.0001210)}}}
{{{highlight(t=ln(5)/0.0001210)}}}