Find the relative rate of change of $f(x)=21+3 e^{-3 x}$. The relative rate of change of $f(x)$ is

Step 1 ：Given the function \(f(x)=21+3 e^{-3 x}\), we are asked to find the relative rate of change.

Step 2 ：The relative rate of change of a function \(f(x)\) is given by the derivative of the function divided by the function itself.

Step 3 ：First, we find the derivative of \(f(x)\), which is \(-9 e^{-3 x}\).

Step 4 ：Then, we divide this derivative by the original function to get the relative rate of change: \(-\frac{9 e^{-3 x}}{21 + 3 e^{-3 x}}\).

Step 5 ：Final Answer: The relative rate of change of \(f(x)=21+3 e^{-3 x}\) is \(\boxed{-\frac{9 e^{-3 x}}{21 + 3 e^{-3 x}}}\).