Question 882113
{{{A=Ie^(-kt)}}} Exponential Decay Equation.
A = final amount
I = initial amount
t time in minutes
k = constant for the specific decaying material


You know these values:
A=21
I=100
-
The 11 minutes half life information allows you to find k.




USE HALF LIFE TO FIND k.
{{{ln(A)=ln(I)+(-kt)ln(e)}}}
{{{ln(A)-ln(I)=-kt*1}}}
{{{kt=ln(I)-ln(A)}}}------you will use this again later.
{{{k=(ln(I)-ln(A))/t}}}
{{{highlight_green(k=(1/t)ln(I/A))}}}---as a formula.
The half-life data meant I=1, A=1/2, t=11.
{{{k=(1/11)ln(1/(1/2))=(1/11)ln(2)}}}
{{{k=0.06301}}}
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Decay Equation Model, {{{highlight_green(A=Ie^(-0.06301t))}}}



USE DECAY EQUATION TO ANSWER t.
Start from {{{kt=ln(I)-ln(A)}}};
{{{highlight(t=(1/k)ln(I/A))}}};
Substitute the known values for k, I, and A; and compute t.
A=21, I=100, k=0.06301.