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Description
When a quantity is increasing in time by the same fraction every period, it is said to exhibit compound growth  every time period it increases by a larger amount.
It is possible to show that the behaviour of the quantity over time follows the law
x(t) = x(0) * exp(r * t)
where

x(t)
is the value of the quantity now 
x(0)
is the value of the quantity at time t = 0 
t
is time in units of [time_period] 
r
is the growth rate in units of 1 / [time_period]
Calculating growth rates
From the equation above, to calculate a growth rate you need to know:
 The value at the start of a period
 The value at the end of a period
 The duration of the period
Then, following some algebra, the growth rate is given by
r = ln(x(t) / x(0)) / t
Example
For a concrete example, assume a table with columns:

num_this_month
 this isx(t)

num_last_month
 this isx(0)
In the following then, growth_rate
is the equivalent yearly growth rate for that month: