I have a 12V DC circuit with input voltage from 2 volts to 5 volts. How can I make the output voltage grow exponentially between the minimum (2volts) and the maximum (5volts) with a coefficient of 1.25 (for example). The key here is that I want the output voltage to be 2 volts when the input is 2 volts, and the maximum of the output voltage should not exceed 5 volts, but anything inbetween should be modulated exponentially. I'm looking for the simplest sollution. Sorry for my amateur question, and thank you in advance!

 

Here is one way to get the exponential function but it will need some work to match your input and output requirements.