When I teach College Algebra at the community college where I work, one of the standard applications in the chapter on exponents and logarithms is half-life. The required text doesn't give the half-life formula above, but instead gives

mass_final = mass_initial * exp(k * t)

and shows how to calculate k by using t_halflife for t (and 1/2 mass_initial for mass_final).

This is a useful general method, but in the course of explaining why radioactive decay is exponential and what half-life means, I naturally derive

mass_final = mass_intial * (1/2) ^ (t / t_halflife),

so I just tell them to use that.

Maybe I'm cheating them because I'm making them do less work, but I like to think that some of them leave the class understanding what the heck a half-life is.