The Collaborative International Dictionary of English v.0.48:

First-order \First`-or"der\, a.
   decaying at an exponential rate; -- a mathematical concept
   applied to various types of decay, such as radioactivity and
   chemical reactions.

   Note: In first order decay, the amount of material decaying
         in a given period of time is directly proportional to
         the amount of material remaining. This may be expressed
         by the differential equation: dA/dt = -kt where dA/dt
         is the rate per unit time at which the quantity (or
         concentration) of material (expressed as A) is
         increasing, t is the time, and k is a constant. The
         minus sign in front of the "kt" assures that the amount
         of material remaining will be decreasing as time
         progresses. A solution of the differential equation to
         give the quantity A shows that: A = e^-kt where e is
         the base for natural logarithms. Thus this type of
         decay is called exponential decay. In certain chemical
         reactions that are in fact second-order, involving two
         reactants, the conditions may be chosen in some cases
         so that one reactant is vastly in excess of the other,
         and its concentration changes very little in the course
         of the reaction, so that the reaction rate will be
         approximately first order in the more dilute reactant;
         such reactions are called pseudo first order.
         [PJC]

The Free On-line Dictionary of Computing (30 December 2018):

first-order

   Not higher-order.

   (1995-03-06)