1. The problem asks for the rate of decay of the function $$f(x) = 500 \left(\frac{1}{4}\right)^x$$. 2. The general form of an exponential decay function is $$f(x) = a(1 - r)^x$$ where $r$ is the decay rate. 3. In the given function, the base is $$\frac{1}{4} = 0.25$$ which can be written as $$1 - r = 0.25$$. 4. To find the decay rate $r$, solve $$r = 1 - 0.25 = 0.75$$. 5. Convert the decay rate to a percentage: $$0.75 \times 100 = 75\%$$. 6. Therefore, the rate of decay is 75%.