Rate of reaction graph
As Curt F. has correctly showed that, in general, if the rate of reaction is plotted against time for an autocatalytic reaction, it would be the shape of curve B (in your question). Since Curt F. has already worked with the mathematical part, only I can do is show you some literature evidence. One of research on an epoxy resin composite hardening (Ref.1) state that:


  Composite structures for aerospace applications are mainly made by the well-known prepreg technology. In order to achieve adequate prepreg processing schedules, and consequently maximum fiber strength utilization, one has to know in deep the cure kinetics of matrix, which held the fibers together. This work describes a procedure to study the cure kinetic and has as example how aromatic amine hardeners influence the cure kinetics of an epoxy resin used in advanced composites. The investigation was carried out by using the DSC technique and it was found that depending on the system used the cure kinetics of the formulation obeys order $n$ or autocatalytic order.






For Comprehensive details for autocatalyzation and review, see Ref.2 &amp; 3.



References:


Michelle L. Costa, Luiz C. Pardini, Mirabel C. Rezende, “Influence of aromatic amine hardeners in the cure kinetics of an epoxy resin used in advanced composites,” Mat. Res. 2005, 8(1), 65–70 (http://dx.doi.org/10.1590/S1516-14392005000100012).
Donna G. Blackmond, “Asymmetric autocatalysis and its implications for the origin of homochirality,” Proc. Natl. Acad. Sci. USA 2004, 101(16), 5732–5736 (https://doi.org/10.1073/pnas.0308363101).
Andrew J. Bissette, Stephen P. Fletcher, “Mechanisms of Autocatalysis,” Angew. Chem. Int. Ed. 2013, 52(49), 12800–12826 (https://doi.org/10.1002/anie.201303822).