To correctly categorize the equations into exponential decay or exponential growth, we analyze their base values. If the base of the exponential term is:

1. Less than 1 (but greater than 0), it represents exponential decay.
2. Greater than 1, it represents exponential growth.

Now, analyzing each equation:

1. $H = 5.9(0.82)^t$: The base $0.82$ is less than 1 → Exponential Decay.
2. $y = 0.8(3.6)^t$: The base $3.6$ is greater than 1 → Exponential Growth.
3. $f(t) = 0.72(15)^t$: The base $15$ is greater than 1 → Exponential Growth.
4. $A = \frac{4}{9}(8)^t$: