Question

What is the correct match?

Answer 1

`y=A(1-r)^t` is exponential decay and `y=A(1+r)^t` is exponential growth.

Explanation:

It depends strongly on context. To make it meaningful, I assume that `y` is a function of `t` and `A,r` are some constants, where `0< r<1`.
When you exponentiate number bigger than 1 you get exponential growth and when the number is less than 1 you get decay. That's why `r>0` part is important. If `r<0` the answers would swap.

If `r=0` you get old boring constant functions.

If `r>1` then `1-r<0` and when you exponentiate negative numbers bad things would happen (if you don't know complex numbers).
Exponentiating 0 is only half-ok. You get 0 for positive t, and whole thing explodes for negative t.

Further interpretations could suggest that `t` is time and `A` is initial value of for example light intensity, electrical current, number of microbes, number of radioactive atoms, money etc.

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