8. {15 pts } A nerve cell receives a synaptic input 0.10cm away from the axon hillock. Activation of the input results in voltage change of +45mV at the site of input. Assume that the length constant () is 300m and action potential threshold at the axon hillock is 50mV. The radius of the dendrite is 500um, and specific membrane resistance Rm is 2000cm2. The passive membrane potentials measured at different locations obeys the following equation: Vm(x)=Vr+Voex, where Vo is the voltage change at the site of innut and the Vr is the resting membrane potential (65mV). a) Determine the membrane voltage at the axon hillock (x=0.10cm). Does the cell fire an action potential as a result of the synaptic input? b) If the radius of the dendrite increases by a factor of 4 , will the length constant () increase or decrease? and by how much