5. A cell receives a synaptic input 100 um away from the axon hillock. Activation of the input results in voltage change of +45mV at the site of input. The voltage response in a passive neuronal process decays with distance exponentially as follows: Vm(x)=V0ex/ You have experimentally determined that length constant () is 100 um and that action potential threshold at the axon hillock is 50mV. Does the cell fire an action potential as a result of the synaptic input? Assume a resting potential of 65mV and no loss of current through the soma. Axon hillock