The exponential growth can be mathematically represented as follows:
$W _{1}= W _{ O } e ^{ rt }$
Here, $W _{1}=$ final size (weight, height, number etc.), $W _{0}=$ initial size at the beginning of the period, $r =$ growth rate, $t =$ time of growth and $e =$ base of natural logarithms. Mathematically, the arithmetic growth rate can be shown as follows:
$L _{ t }= L _{0}+ r t .$
Here, $L _{ t }$ is the length at time $t , L _{0}$ is length at time 0 and $r$ is the rate per unit time.