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Exponent growth follows a relation represented by y = a * exp(b*t), where y is a function of time, a and b are constants, and t is the time variable.
With formal math out of the way, let us have a feel of what it means in real values. Let a = 1 = b to simplify calculations.
Therefore, y = e^t. I am going to tabulate the value of y for the first few minutes. You can plug the formula into Excel to replicate the result.
t [s] y(t)
==
0 1
1 2.718
2 7.389
3 20.086
4 54.598
5 148.413
We observe that y(t+1) = 2.718*y(t). That means the y value at (t+1) s is equal to 2.718 times the y value one second before. At this rate, a handheld calculator will give up at t=231 s. That is exponential growth.
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