Growth factors activate Ras, PI3K and other signaling pathways. It is not well understood how these signals are translated into a decision of individual cells to proliferate or differentiate. Using single-cell image analysis of nerve growth factor (NGF)-stimulated PC12 cells, we discovered a two-dimensional phospho-ERK (pERK)-phospho-AKT (pAKT) response map with a curved boundary that separates differentiating from proliferating cells. The boundary position stayed invariant when we used different stimuli or perturbed upstream signaling components. We further identified Rasa2 as a negative feedback regulator that links PI3K to Ras to place the center of a stochastically distributed pERK-pAKT signals close to the decision boundary. This allowed a uniform NGF stimulus to trigger a subpopulation of cells to differentiate with each cycle of proliferation. Thus, by linking a complex signaling system to a simpler intermediate response map, cells gain unique control capabilities to balance cell number expansion with differentiation.