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To solve the problem of calculating the average rate of change for the given function over the interval \([0, 3]\), we can use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \(a\) and \(b\) are the endpoints of the interval.

For this problem:
- \(a = 0\) and \(b = 3\),
- \(f(0) = 4\) and \(f(3) = 14\).

Now, applying these values to the formula:

\[
\text{Average Rate of Change} = \frac{f(3) - f(0)}{3 - 0} = \frac{14 - 4}{3} = \frac{10}{3} \approx 3.33
\]

Thus, the average rate of change over the interval \([0, 3]\) is approximately **3.33**.

Would you like further details or explanations on this? Here are some related questions:

1. How is the average rate of change different from instantaneous rate of change?
2. Can the average rate of change be interpreted as a slope in this context?
3. How do you calculate the rate of change for non-linear functions?
4. What happens if the interval is negative or includes negative values of \(x\)?
5. How does this concept apply to velocity in physics?

**Tip:** When calculating average rates of change, think of it as the slope of the secant line between two points on a graph.

Calculate the average rate of change of the given function over the given interval [0, 3].

Learn how to calculate the average rate of change for a function using data points over the interval [0, 3]. This problem demonstrates the application of basic algebraic concepts and the formula for average rate of change.

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