equation solving – Finding the coefficients of an expression

I have a set of formulas of the following form:

{5.1011 + E^(-6876.32 t) (-5.1011 + 1. x), 
 5.28335 + E^(-4868.36 t) (-5.28335 + 1. x), 
 6.45616 + E^(-1847.14 t) (-6.45616 + 1. x), 
 144.165 + E^(-34.6815 t) (-144.165 + 1. x), 
 320. + E^(-15.6055 t) (-320. + 1. x)}

I would like to get the coefficients {a, b, c} where each of the formulas is expressed as

a + e^(b*t)*(c + 1.` vStart)

I tried using rules, “Normal”, and Solve to see if I could figure this out. I will note that if I take any of these expressions and for example do this:

5.1011 + E^(-6876.32 t) (-5.1011 + 1. x) //TreeForm

I get a picture like this:
TreeForm of equation

so Mathematica clearly understands the pieces. I just cannot figure out how to turn this into the list shown with TreeForm so I can grab the pieces. As an example, in this tree (simplifying each coefficient), I’d get a=5.1, b=-6876.3, c=-5.1.

I suspect this is something simple but am at a loss. Any help appreciated.