By Charge Control equation determine collector current

Question

In the individual transistor inverter circuit demonstrated below, the input voltage is switched abruptly by Vcc to 0V. There base current as acquired from the Charge Control equations governing turn-off of the transistor is specified as:

I_B = (τ_F/τ_BF) i_C + (τ_F/τ_BF) C_BCR_C (di_c/dt) + τ_F(di_c/dt) + C_BCR_C(di_c/dt) = - V_{BE ON}/R_B

Determine this equation to acquire an expression for the collector current and the output voltage of the inverter throughout turn-off of the transistor. Therefore evaluate the 10 to 90 percent rise-time of the output voltage of the inverter when τ_F = 0.2ns, β_F = 50, R_C = 1kΩ, R_B = 10kΩ and C_BC = 0.5pF as well as V_CC = 5V.