Question 843241
Solve this generally for k:  {{{A=Qe^(-kt)}}};

Let t=5, A=(1/2)Q, , and find the formula this way for k.

Rewrite {{{A=1800e^(-k*t)}}} using the value you found for k.



Best if you follow that and do it.
I did not show you the specific steps.  Do you need them?



SOLUTION WITH NEARLY ALL STEPS SHOWN--------------------------------

{{{highlight_green(A=Qe^(-kt))}}}------Basic Model for Decay
{{{ln(A)=ln(Q)+ln(e^(-kt))}}}
{{{ln(A)-ln(Q)=-kt*1}}}
{{{highlight_green(k=(ln(Q)-ln(A))/t)}}}


The specific example has initial half life of 5 years, t=5 with {{{A=Q/2}}}, enough for finding the value of k.
{{{k=ln(Q/A)/t}}}
{{{k=ln(Q/(Q/2))/5}}}
{{{highlight_green(k=ln(2)/5)}}}
But as a decimal number, this can be stated {{{highlight(k=0.1386)}}}


The specific model equation based on given Q=1800 and the found value for k, becomes {{{highlight(highlight(A=1800*e^(-0.1386*t)))}}}