Given measurements of a reporter gene at two different times, and knowing the half-life stability of the reporter protein, calculate the rate at which the gene is being produced.

rate = q(A - A₀e^-qt)/(1 - e^-qt)

A: amount of reporter (final)
A₀: amount of reporter (initial)
t: time interval between A and A₀
q: ln2/reporter half-life (in the same units as t)