As time goes on, the balloon gets closer and closer to the ground, or it's at a lower altitude. This means that the altitude depends on how much time has passed. Since you can use the variable t to predict the altitude, just as you would use the amount of time that has passed, t actually is the amount of time that has passed. Therefore t represents time.
I said before that you can predict the height using time. In this equations, there are only two unknowns: the amount of time that has passed, and the height. Since we already know time is represented by "t", we can figure that a(t) represents the height after any specific time. Think of a(t) as the y value, and t as the x value. We need to find x first in order to find y, just like we need a specific t-value (time) to find the height at that time. This is why the y value, a(t), is written like it is, because the altitude (a) is found by plugging in a time (t). So a(t) is the altitude of the balloon.
We already know that a(t) is the altitude at any time. a(5.5) is the altitude at a very specific time, or the altitude of the balloon at 5.5 minutes.
