A region of space contains a changing magnetic field given by \(\vec{B}(t)=B_{0} e^{-t / \tau} \hat{k}\), and a circular conducting loop of radius \(R\) lies in this region in the \(x y\) plane. 

(a) Calculate the upward magnetic flux through the loop as a function of time. Is the flux increasing or decreasing as time passes? 

(b) Calculate the induced emf in the loop as a function of time, where upward is in the \(\hat{k}\) direction.

(c) Determine the current direction in the loop.