Find the average rate of change of the function \( f(x)=\sqrt{x} \) from \( x_{1}=16 \) to \( x_{2}=25 \). 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 \( x_1 = 16 \) to \( x_2 = 25 \), we use the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] First, we calculate \( f(16) \) and \( f(25) \): \[ f(16) = \sqrt{16} = 4 \] \[ f(25) = \sqrt{25} = 5 \] Now we can plug these values into our formula: \[ \text{Average Rate of Change} = \frac{5 - 4}{25 - 16} = \frac{1}{9} \] So, the average rate of change is \( \frac{1}{9} \).