A cell is driven by current i(t)=u(t). Its linear membrane model has impulse response $h(t)=Ae^{-t/\tau}u(t)$, with A=−34 V/s and τ=3 ms. Find membrane-voltage output at 5 ms in mV.
The response to a unit step is the integral of the impulse response: v(t)=Aτ(1−e⁻ᵗ/τ)u(t). At five milliseconds, v=−34×.003×[1−exp(−5/3)] V≈−.082735 V. Converting to millivolts gives approximately −82.7 mV, within the published −84 to −81 interval.
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