t: is the time in seconds since the start of Advent.

k: is a constant calculated from the equation k=log(N)/(t_f * log(2))

Where

N is the total number of lights you have and

T_f is the total length of Advent in seconds.

Because N and T_f could change, k is specific to whatever your setup is.

That way 2^(k*t_f) = N i.e. at the end of Advent all your lights are on.