Exponential decay with many rates

The general model for an exponential decay is:

$\displaystyle M(t) = M_0 e^{-\lambda t}, $

where $\displaystyle \lambda$ is the decay rate. There exist natural process with multiple decay rates, also known as decay modes, which transform the model above into the following:

$\displaystyle M(t) = M_0 e^{-(\lambda_1 + \lambda_2 + \dots + \lambda_{n}) t}, $

My question is simple: does anyone know of any examples involving many decay constants? Equivalent examples for the exponential growth case are equally appreciated.