Question 1026381
For exponential decay/growth the basic model is {{{P=P[0]e^(rt) = 250e^(rt)}}}.

After 12 hours, the equation becomes {{{230 = 250e^(12r)}}}

==> {{{0.92 = e^(12r)}}} ==> ln0.92 = 12r, or {{{r = ln0.92/12}}}.

==> {{{P=P[0]e^(rt) = 250e^(rt) = 250e^(tln0.92/12) = 250*0.92^(t/12)}}}, or

{{{P = 250*.92^(t/12)}}}.
To find the half-life set P=125 (half of 250.)

==> {{{125 = 250*.92^(t/12)}}}.
==> {{{0.5 = 0.92^(t/12)}}}  ==> {{{t = -12log2/log0.92}}}

==> t = 99.8, or 100 hours, rounded off to the nearest whole number.