Question 952918
Basic Model: {{{highlight_green(y=p*e^(-kt))}}}


The one-seventh life is 4 years.


Find logarithms of both sides.
{{{ln(y)=ln(p)-kt}}}
{{{kt=ln(p)-ln(y)}}}
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You can find two formulas from that step:
{{{k=(ln(p)-ln(y))/t}}}   and    {{{t=(ln(p)-ln(y))/k}}}


FIND THE DECAY CONSTANT k.

{{{k=(ln(1)-ln(1/7))/4}}}


{{{k=(ln(1/(1/7)))/4}}}


{{{k=ln(7)/4}}}


FIND THE HALF-LIFE {{{t[1/2]}}}.

{{{t[1/2]=(ln(p/y))/k}}}


{{{ln(1/(1/2))/(ln(7)/4)}}}


{{{ln(2)(4/ln(7))}}}


{{{highlight(4((ln(2))/(ln(7))))}}}, years