Find the average rate of change of the function \( f(x)=\sqrt{x} \) from \( x_{1}=100 \) to \( x_{2}=121 \). The average rate of change is \( \square \). (Simplify your answer.)

To find the average rate of change of the function \( f(x) = \sqrt{x} \) from \( x_1 = 100 \) to \( x_2 = 121 \), we use the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] First, calculate \( f(x_1) \) and \( f(x_2) \): \[ f(100) = \sqrt{100} = 10 \] \[ f(121) = \sqrt{121} = 11 \] Now, substitute these values into the formula: \[ \text{Average Rate of Change} = \frac{11 - 10}{121 - 100} = \frac{1}{21} \] Thus, the average rate of change is \( \frac{1}{21} \).