Question 256914
Half life means half of the original amount remains.
{{{dm/dt=-0.005m}}}
{{{dm/m=-0.005*dt}}}
Integrate,
{{{ln(m)=-0.005t+C}}}
{{{m=Ce^(-0.005t)}}}
where C=m0 when t=0, the original amount of material. 
{{{m=m0*e^(-0.005t)}}}
At {{{t=0}}}, {{{m=m0}}}
When {{{t=t_h}}}, {{{m=(1/2)m0}}}
Substitute,
{{{(1/2)m0=m0*e^(-0.005(t_h))}}}
{{{1/2=e^(-0.005(t_h))}}}
{{{ln(1/2)=-0.005(t_h)}}}
{{{t_h=(ln(1/2)/(-(0.005)))}}}
t_h=138.6 years, approximately