Your adjustable gain amplifier may use any type of transistor. Here are some questions to stimulate your thinking on which way to go:
- what determines the voltage gain of a simple common emitter amplifier using an NPN transistor, like a 2n3904 for example?
- what determines the voltage gain of a simple common source amplifier using an FET, like a 2N7002 for example?
- knowing which elements control the voltage gain, how could you vary those elements electronically?
- by answering the previous question, do you have an impression that the NPN transistor amplifier would be easier or more difficult than the FET amplifier to vary the gain of electronically?
Your reply to these questions will lead to the next stage of help.