An npn BJT with grounded emitter is operated with $V_{B E}$ $=0.700 \mathrm{V},$ at which the collector current is $0.5 \mathrm{mA}$. A $10-\mathrm{k} \Omega$ resistor connects the collector to a +10 -V supply. What is the resulting collector voltage $V_{C} ?$ Now, if a signal applied to the base raises $v_{B E}$ to $705 \mathrm{mV}$, find the resulting total collector current $i_{c}$ and total collector voltage $v_{c}$ using the exponential $i_{c}-v_{B E}$ relationship. For this situation, what are $v_{b c}$ and $v_{c}$ ? Calculate the voltage gain $v_{c} / v_{b e}$. Compare with the value obtained using the small-signal approximation, that is, $-g_{m} R_{C}$.