Find the average value of the function $g(x)=3 e^{x}-5$ on the interval $[-2,4]$. Round your answer to 2 decimal places.

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 ：We need to find the average value of the function \(g(x)=3e^{x}-5\) on the interval \([-2,4]\).

Step 3 ：First, calculate the integral of \(g(x)\) from \(-2\) to \(4\).

Step 4 ：Then, divide the result by the length of the interval, which is \(4 - (-2) = 6\).

Step 5 ：By doing the calculations, we find that the average value is approximately 22.2314073749538.

Step 6 ：Rounding to two decimal places, we get \(\boxed{22.23}\).