Question 936000
General model is {{{N=N[o]e^(-kt)}}}



{{{ln(N)=ln(N[o])-kt}}}
{{{ln(N)-ln(N[o])=-kt}}}
{{{kt=ln(N[o])-ln(N)}}}
{{{k=(1/t)ln(N[o]/ln(N))}}}------use this to find the value for k.


{{{k=(1/45)(ln(160/20))}}}
{{{k=(1/45)ln(8)}}}
{{{highlight(k=0.046)}}}


You can return to this one, {{{kt=ln(N[o])-ln(N)}}} , to determine the half-life.
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{{{t=(1/k)ln(N[o]/N)}}}
{{{t=(1/k)ln(2)}}}
{{{t=(1/0.046)ln(2)}}}
{{{highlight(t[half]=15.07)}}}, maybe more accuracy than reasonable.


Your more specific decay model is  {{{N=N[o]e^(-0.046t)}}}.
Now you have a known N but you want to solve for {{{N[o]}}}.