# Math Help - Exponential decay with many rates

1. ## Exponential decay with many rates

The general model for an exponential decay is:

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

where $\lambda$ 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:

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

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

2. Has anybody ever encountered a problem (both in social and natural sciences) related to multiple rates of exponential growth or decay?