To find the rate of change of y with respect to time t, we need to take the derivative of the function y = 500(1-0.2)^t with respect to t:
dy/dt = 500*(-0.2)*(1-0.2)^(t-1)
Simplifying this expression, we get:
dy/dt = -100(0.8)^t
Therefore, the rate of change of y with respect to t is given by -100(0.8)^t. This means that the rate of change of y decreases exponentially over time, and approaches zero as t becomes large.