Finding induced emf in a decaying inductor current

[r_swayze]

Homework Statement

The current in a 4.70 mH inductor decays over time according to the following function, where t is in seconds.

I(t) = (.943A) e^{-(396 s-1) t)}

(a) What is the induced emf across the inductor at t= 5.00 ms? (b) How long does it take the emf to drop below 1.25 mV?

The Attempt at a Solution

Since emf = -L(dI/dt) , I can take the derivative of the function above and plug in t=.005, right?

I' = (.943A) e^{-(396 s-1) t)} (-1/396s)

Plug in t=.005 and I get I' = -.00238

emf = -L(dI/dt)

emf = -(.0047)(-.00238) = 1.119x10^-5

I tried this answer but it was incorrect. What am I doing wrong?

 

[rl.bhat]

You have not taken into account the term e^-396*t.