Cells sense information encoded in extracellular ligand concentrations and process it using intracellular signalling cascades. Using mathematical modelling and high-throughput imaging of individual cells, we studied how a transient extracellular growth factor signal is sensed by the epidermal growth factor receptor system, processed by downstream signalling, and transmitted to the nucleus. We found that transient epidermal growth factor signals are linearly translated into an activated epidermal growth factor receptor integrated over time. This allows us to generate a simplified model of receptor signaling where the receptor acts as a perfect sensor of extracellular information, while the nonlinear input-output relationship of EGF-EGFR triggered signalling is a consequence of the downstream MAPK cascade alone.