  We define formal exponential maps for any graded manifold as maps from the
formal tangent bundle (that we also define) into the graded manifold. We show
that each such map uniquely determines and is determined by its associated
Grothendieck connection, which is shown to be flat, and to furnish a resolution
of the ring of functions. We then show how a recent construction involving the
data of a connection on the tangent bundle recovers a large class of formal
exponentials in our definition.
  As an application, we use a formal exponential map to linearise a QP-manifold
at a point. This gives the formal tangent space at each point the structure of
an $L_\infty$-algebra with invariant inner product.
