Sensor Signal Calibration (Electrical & Systems Engineering)

Engineers design sensor systems (like pressure transducers or temperature sensors) by chaining multiple physical operations together. For example, an industrial pressure sensor converts a physical pressure input $P$ (in psi) into a voltage signal $V$ (in volts) using a linear calibration function:

This voltage is then fed into an Analog-to-Digital Converter (ADC) that maps the voltage to a 10-bit digital value $D$ represented by the function:

1. Find the composite function $(D \circ V)(P)$ that directly maps physical pressure $P$ to the digital output $D$.
2. Solve for the exact pressure $P$ (in psi) that will cause the digital output to reach a threshold alarm value of $D = 800$.