Question 1206895
{{{y=pe^(-kt)}}}


If,...
{{{150=250e^(-k*30)}}}

{{{ln(150)=ln(250)+(-30k)*ln(e)}}}

{{{-30k+ln(250)=ln(150)}}}

{{{-30k=ln(150)-ln(250)}}}

{{{k=(ln(250)-ln(150))/30}}}

{{{k=(1/30)(ln(25/15))}}}

{{{k=(1/30)(ln(5/3))}}}

{{{highlight_green(k=0.017028)}}}


Half-Life?
{{{1/2=1*e^(-xk)}}}

{{{ln(1/2)=ln(e^(-x*0.017028))}}}

{{{-ln(2)=-0.017028x*ln(e)}}}

{{{0.017028x*1=ln(2)}}}

{{{highlight_green(x=ln(2)/0.017028)}}}

{{{highlight(x_halflife=40.7)}}}---------To 2 decimal  places?   40.71 years