Show that `N=(N_(0))/(2^(n))` where n = number of half lives n=t/T

Explanation

Let `N_(0)` be the initial a number of atoms be present in the sample . The number of half lives `n=t//T` where 'T' is the half period.
During the first half life period ,
`N(N_(0))/(2^(1))`
During the second half life period,
`N=(1)/(2)=(N_(0)/(2))=(N_(0)/(2^(2)))`
Similarly during the 'n' half life period,
`N=(N_(0)/(2^(n)))`