Concave Upper Bound of Linear Combination of Exponential function

Question

I have $f(x)=a_1e^{b_1 x}+...+a_Ne^{b_N x}$

where $ a_i\in \mathbb{R} \ \forall i$, $b_i\in \mathbb{R_+} \ \forall i$

and N is a finite integer.

Is there any concave function that upper bound $f(x)$ for $x<0$?