Proving that the water leaving a vertical pipe is exponential (decay)

How can I prove that the rate of which water leaves a vertical cylindrical container (through a hole at the bottom) is exponential of the form :

$A{e}^{kx}$

I know that Torricelli's law is:

$\sqrt{2gh}$

But this only proves a square root relationship. I have data points every 10 seconds and graphed it suggests a decay function. I know the distance between the pipe is 1.5M and the internal diameter is 5cm. The hole diameter is 0.25cm, if this helps. I need to prove that the water leaving the pipe is exponentially decaying.

How can I prove that the rate of which water leaves a vertical cylindrical container (through a hole at the bottom) is exponential of the form :

$A{e}^{kx}$

I know that Torricelli's law is:

$\sqrt{2gh}$

But this only proves a square root relationship. I have data points every 10 seconds and graphed it suggests a decay function. I know the distance between the pipe is 1.5M and the internal diameter is 5cm. The hole diameter is 0.25cm, if this helps. I need to prove that the water leaving the pipe is exponentially decaying.