How does a transistor work as a switch?

Transistors are commonly used as electronic switches, for both high power applications including switched-mode power supplies and low power applications such as logic gates.
When the transistor reaches a base voltage of a certain level the current will no longer increase and the output will be held at a fixed voltage. Because of this property the transistor can have values of input voltage such that the output is either completely off or completely on. The transistor is acting as a switch, and this type of operation is common in digital circuits where only "on" and "off" values are relevant.
FOR A TRANSISTOR TO BE CALLED A SWITCH it must be operating into the saturation area. whereby both diodes are fully forward biased. to saturate a transistor Essex current must flow into the base. how much rules of thumbs beta of 10. Pushing more base current will have the effect of increasing saturation voltage meaning there is a trade off. it is incorrect to assume that the voltage will no longer increase I submit that both diodes will follow an exponential curve.