Approximation the function $f(t)=I_0(-rt)e^{-rt}$ with sum of Exponentials.

Question

Consider the function $f(t)=I_0(-rt)e^{-rt}$ where $I_0(t)$ is modified Bessel’s function and $r>0$. I am looking for an approximation for the function with a sum of exponential functions in $t \in [0,T=100]$ with error less than $10^{-2 } or10^{-3 }$. I mean I want to approximate the function by $$\sum_{i=0 \ or \ 1}^{\infty \ or \ m} a_i e^{b_it}$$ which $a_i$ and $b_i$ are real. It would be appreciated if someone can help me. Thanks