A flat, circular, aluminum loop with a radius of $75$ cm is at rest in a uniform magnetic field, as shown in the edgeon view in the figure. The field is changing with time according to B$($t$)=(1\mathrm{.}4$T$)$e$-\mathrm{.}057$t$.$ The aluminum loop has a resistance of $0\mathrm{.}120.$

a$.$ Find the emf induced in the loop as a function of time, assuming t is in seconds. b$.$ What is the direction of the induced current in the loop, as viewed from below the loop. c$.$ What is the magnitude of the induced current at t $=5\mathrm{.}0$ s$?$