Find the average value of the function on the given interval. \[ f(x)=e^{x / 9} ;[4,9] \] The average value is $\square$. (Round to three decimal places as needed.)

Step 1 ：The average value of a function \(f(x)\) on the interval \([a, b]\) is given by the formula: \(\frac{1}{b - a} \int_{a}^{b} f(x) dx\)

Step 2 ：Here, our function \(f(x) = e^{\frac{x}{9}}\) and the interval is \([4, 9]\). So, we need to calculate the integral of \(e^{\frac{x}{9}}\) from 4 to 9 and then divide by \((9 - 4)\).

Step 3 ：Calculate the integral of \(e^{\frac{x}{9}}\) from 4 to 9: \(\int_{4}^{9} e^{\frac{x}{9}} dx = 9[e^{\frac{x}{9}}]_{4}^{9} = 9[e^{\frac{9}{9}} - e^{\frac{4}{9}}] = 9[e - e^{\frac{4}{9}}]\)

Step 4 ：Divide by \((9 - 4) = 5\): Average value = \(\frac{1}{5} * 9[e - e^{\frac{4}{9}}] = 1.8[e - e^{\frac{4}{9}}]\)

Step 5 ：Substitute the values of \(e\) (approximately 2.71828) and \(e^{\frac{4}{9}}\) (approximately 1.65399) into the equation: Average value = \(1.8[2.71828 - 1.65399] = 1.8[1.06429] = 1.916\)

Step 6 ：So, the average value of the function on the given interval is approximately \(\boxed{1.916}\) (rounded to three decimal places).