a$)$ From the circuit, show that: $(1)/(2\backslash$pi f$\_($T$))=\backslash$tau $\_($F$)+($kT$)/($qI$\_($C$))[$C$\_($dBE$)+$C$\_($dBC$)]$

b$)$ Analyze which physical parameters can be modified to increase the FT$.$

c$)$ Develop a python code that generates the Ic vs fT curve.

$($Note: develop the mathematics and explanation that support your answer for the physical parameters that can be modified to increase the fT$,$ keep in mind that IC is involved. Exercise taken from the book Analysis and Design of Analog Integrated Circuits, $5$th Edition, Page $51).$