Estimate maximum tolerable load capacitance

Question

In the capacitively loaded individual transistor inverter demonstrated below, the input voltage is switched abruptly from V_CC to 0Volt at time t = 0. In that case the transistor is assumed to function as an ideal change, draw the waveform of the output voltage like a function of time and determine an expression for this voltage. Thus, derive an expression for the low-to-high propagation delay of the inverter within terms of the circuit parameters. 

Estimate the maximum tolerable load capacitance when this propagation delay is not to exceed 10ns while β_F = 50, R_C = 1kΩ, R_B = 10kΩ and V_CC = 5V.