$(35$ points$)$ The circuit in Figure $2$ has a BJT transistor with its characterized $I_C$ vs $V_{CE}$ dependence for an $I_B$ for which the transistor is biased to in the circuit. Determine:

a$.I_C,I_B,V_B,V_C,$ and $V_E.$

b$.$ What region of operation is the transistor in$?$

c$.$ Draw a load line for the $7$ k resistor against the $I_C$ vs $V_{CE}$ transistor characteristic.

Figure $2,$ Problem $2$