Find the associated half-life time or doubling time:
Q = 1200e−0.025t
The way you have your formula written, t is for half-life, which is the exact opposite of doubling time!
Solve for t over the real numbers:
1200/e^(0.025 t) = 600
1200/e^(0.025 t) = 1200 e^(-t/40):
1200/e^(t/40) = 600
Divide both sides by 1200:
e^(-t/40) = 1/2
Take reciprocals of both sides:
e^(t/40) = 2
Take the natural logarithm of both sides:
t/40 = log(2)
Multiply both sides by 40:
t = 40 log(2) =~ 27.726 Time units.