How to determine exponential decay rate of sum of sines function when the time constant is different for each exponential?

Question

I will show you my MATLAB code:

t = 0:0.1:10*pi;
test_sine = exp(-0.1*t).*sin(t) + exp(-0.2*t).*sin(2*t);

The time constant for each of my sine waves are different, but I would like to know how I would go about determining what the decay rate is for my test_sine function.