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 âtâ days. (2 marks)
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. Without using the log function.
If you were to take 200 milligrams of Advil how many milligrams will remain in the
body 10 hours later? Answer to two decimal places. Show your workings in
detail using the equation
Without the log function
a) The half life formula can be written as M(t) = M0 * (1/2)^(t/4), where M(t) is the amount of Advil material in milligrams that remains after "t" days, M0 is the original sample size (200 milligrams in this case), and t is the time in hours.
b) To determine how long it takes for the sample to decay to 50 milligrams, we set M(t) = 50 and solve for t:
50 = 200 * (1/2)^(t/4)
1/4 = (1/2)^(t/4)
2 = 1/2^(t/4)
2 = 2^(-t/4)
Since 2 = 2^1, we can say that t/4 = 1, so t = 4. Therefore, it takes 4 hours for the sample to decay to 50 milligrams.
c) To determine how many milligrams will remain in the body 10 hours later, we set t = 10 in the equation:
M(10) = 200 * (1/2)^(10/4)
M(10) = 200 * (1/2)^2.5
M(10) = 200 * 0.1768
M(10) = 35.36
Therefore, 35.36 milligrams of Advil will remain in the body 10 hours later.