Physics Question (Damped Oscillator)

[wademay4]

Question:

A 50.0 g hard-boiled egg moves on the end of a spring with force constant k = 25.0 N/m. It is released with an amplitude 0.300 m. A damping force F_x = -bv acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m. Calculate the magnitude of the damping coefficient b.

Attempt/Idea:
I'm not really sure what exactly to do here. I know the oscillator has to be underdamped, and I know the general equation for harmonic motion of an underdamped oscillator is Ae^(-bt/2m)cos(omega*t+theta). I also know that omega in this particular instance is equal to sqrt(k/m-b^2/4m).I'm thinking that I find some sort of equation for the Amplitude as a function of time, and then use that to solve for b. Once I do that, I find that A(t)= A_initial*e^(-bt/2m). I know I have to set up some sort of equation to solve for b, but I'm not sure how I these equations relate to each other. Any hints or suggestions would be greatly appreciated.