Imagine you have bacteria that divides into 2 every hour.
If at #T=0# we have one such bacteria, at #T=1# (in an hour) we will have two of them, at #T=2# (in two hours) we will have 4 of them etc.
At any time #T# we will have the number of bacteria equal to
The above is a typical exponential growth of a population. The number of off-springs and other parameters can modify the formula, but it still will be based on exponential function with the time parameter in the exponent.
Obviously, real life conditions introduce complications in the formula based on variable productiveness and mortality rates.