the time that has been given to you in the question don't really mean a thing, other than to test your understanding of half-life. radioactive substance decay with a constant half-life. eg. if substance A decays radioactively to form substance B, and its half-life is 8days, then if you have 8g of substance A at day 1, then it means by 8th day, your sample would now contain 4g (ie. 1/2 of 8g) of substance A, but the sample you have now is a mixture of A and B. radioactive is a continuous decay phenomena.
are you familiar with calculus? radioactive decays is a first order rate equation, which you can integrate to obtain the decay profile.
radioactivity is directly proportional number of radioactive atoms
let N be number of radioactive atoms
dN/dt = -kN
(1/N)dN/dt = -k
integrate LHS and RHS with respect to time
ln N = -kt + C (constant of integration)
when t = 0, ln No = C where No is the initial number of radioactive atoms.
therefore, ln N - ln No = -kt => ln (N/No) = -kt
half-life of a substance (t1/2) is given by:
N/No = 1/2 => - ln2 = -kt1/2
t1/2 = (ln 2)/k
k = ln 2 / t1/2
the decay profile is thus:
ln (N/No) = -kt
ln (N/No) = -(ln 2 / t1/2)t
thus by knowing the half life, you can calculate the decay constant (k) and thus obtain the fill decay profile of the substance of interest.