The situation described involves exponential growth, as modeled by the function \( a(t) = 5000(1.12)^t \). In such a model, the amount \( a \) increases over time, and typically, it increases slowly at first and then more rapidly as time progresses, due to the compounding effect of the growth rate.
Therefore, the true statement about the graph of the function is:
As t increases, a increases slowly at first and then quickly.