An ideal detector calibration is an affine map. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Calibration starts from the net count
After dark subtraction, the net signal is 12.
Cnet=12
Gain and offset make an affine output
The gain is 2 and the offset is 1, so the output is 25.