Question 1171697

A certain pain reliever has a half-life of 16 hours. If the initial plasma level of this pain reliever, given as a single dose, is 512mg/L, how long will it take for the plasma level to fall to 16mg/L?
<pre>It's not nearly as complex as the other person makes it out to be.
With ½-life being 16 hours, DECAY CONSTANT, or {{{matrix(1,5, k, "=", ln(1/2)/16, "=", - .04332)}}}
The CONTINUOUS GROWTH/DECAY formula: {{{matrix(1,3, A, "=", A[o]e^(kt))}}},  then becomes: {{{matrix(1,3, 16, "=", 512e^(- .04332t))}}}
{{{matrix(1,3, - .04332t, "=", ln(16/512))}}} ------- Converting to LOGARITHMIC (Natural) form
{{{matrix(1,3, - .04332t, "=", ln(1/32))}}}
Time taken for the plasma level to fall to 16 mg/L, or {{{highlight_green(matrix(1,7, t, "=", ln(1/32)/(- .04332), "=", 80, hours, "(approximately)"))}}}