First look at what you are analyzing, this is a first order reaction.

So you know

t_{1/2} = 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=k[A]

into

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

ln[A/A_{o}]=-kt

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.