Advil that has a half life of 4 hours. What this means is that after this
time there is only half of the amount of Advil left in a sample is half of
its original amount.
a) If the original sample size was 200 milligrams, write an equation using the half
life formula that will represent the M, of the Advil material in milligrams that
remains after “t” days.
b) Use this equation to determine exactly how long it takes for the same to decay
to 50 milligrams. Show your workings in detail using the equation
a) The half life formula can be written as:
M(t) = M(0) * (1/2)^(t/4)
Where:
M(t) = amount of Advil left after t hours
M(0) = original amount of Advil (200 mg)
t = time in hours
Substitute M(0) = 200 mg into the formula:
M(t) = 200 * (1/2)^(t/4)
b) To determine how long it takes for the amount of Advil to decay to 50 mg, we set M(t) equal to 50 mg and solve for t:
50 = 200 * (1/2)^(t/4)
1/4 = (1/2)^(t/4)
Taking the log of both sides:
log(1/4) = log((1/2)^(t/4))
log(1/4) = (t/4) * log(1/2)
log(1/4) = -(t/4)*log(2)
t/4 = log(4)/log(2)
t = 4 * log(4)/log(2)
t ≈ 5.322 hours
Therefore, it takes approximately 5.322 hours for the amount of Advil to decay to 50 mg.