I have a general question about whether you can usually use either formula, A(t) = Ae^(kt), or A(t) = Ab^t, in exponential decay (half-life) word problems, or if there is some difference in where each of these formulas is applicable. I'm used to using A(t) = Ae^(kt) for everything, but I saw some resources on the web and videos where A=Ab^t was used (also, A=A(1+r)^t)
You can convert between them. Forget the "A" for now; just do the e^(kt), b^t, and (1+r)^t.
e^(kt) = (e^k)^t = b^t for b = e^k
(1+r)^t = b^t for b = 1 + r
So you can use any of them. But I've mostly seen e^(kt) for half-life stuff. Unless your book tells you to use b^t, I'd stick with e^(kt). That's also the one they'll want in your science classes. Like if you do chemistry or something. The (1+r)^t is usually really (1 + r/n)^(nt) for n-percent interest compounded n times per year for t years.