Figure $3$: Circuit for Problem $3.$

Problem $3$: Application$-15\%$

Consider the ideal op$-$amp circuit shown in Figure $3.$

a$)$ Write an expression for the relationship between $v_{\text{o}\text{u}\text{t}}$ and $v_{in}.$

b$)$ What is $v_{\text{o}\text{u}\text{t}}$ when $v_{in}=0\mathrm{.}2V?$

c$)$ What function does the circuit perform? What is a real$-$world application that this circuit would be useful for?