Question 1048723
{{{y=p*e^(-kt)}}}--------exponential decay model


Need find k.  The variable to find, AFTER k is found, will be t.


HALF LIFE
{{{p/2=p*e^(-k*8)}}}
{{{(1/2)=e^(-8k)}}}
{{{ln(1/2)=ln(e^(-8k))}}}
{{{-8k*ln(e)=ln(1/2)}}}
{{{-8k=-ln(2)}}}
{{{highlight_green(k=ln(2)/8)}}}
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You would like to put a decimal number to that.
{{{k=0.08664}}}, but remember to include the negative sign in the model!!


WHEN THE 5 GRAMS BECOME 1 GRAM?  FIND t.
{{{ln(y)=ln(p*e^(-kt))}}}
{{{ln(p)-kt=ln(y)}}}
{{{-kt=ln(y)-ln(p)}}}
{{{-kt=ln(y/p)}}}
{{{t=(-1/k)ln(y/p)}}}
{{{highlight(t=(1/k)ln(p/y))}}}, if you want to keep the positive value of k found earlier.


YOU FINISH IT.
{{{system(p=5,y=1,k=0.08664,t=YouNeedToEvaluateHours)}}}