First look at what you are analyzing, this is a first order reaction.
So you know
t1/2 = ln(2)/k
You are told the half-life, and ln(2) is just a number, so solve for k (rate constant for first order reaction).
I do not know if you have had calculus, or are taking a class that employees calculus.
But after a little math, you can turn your
R=-d[A]/dt (this is in terms of time derivative, which a derivative is a rate of change)
Setting them equal,
d[A]/dt = -k[A]
Integrating both side with proper bounds of integration, and then some algebra you can get to this equation (which you might/should recognize):
ln[A] = ln[A]o-kT
Which with some algebra turns into
You know k, so you can easily solve for t.
Because of the derivation of the equation, it matters not if it is the concentration or the activity.
Note, A sub 0 ([A]o) is initial.
And none of these equations hold true for a second order reaction.