Estimate, to two significant figures, the average rate of change of government funding for the arts over the period [0, 8]. (Be careful to state the units of measurement.) 0= 1.5 and 8= 1.3

To estimate the average rate of change of government funding for the arts over the period \([0, 8]\), we use the formula for the average rate of change:

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

Where:
- \(f(a)\) is the function value at the start of the interval \(a = 0\)
- \(f(b)\) is the function value at the end of the interval \(b = 8\)
- \(b - a\) is the length of the interval

Given:
- \(f(0) = 1.5\) (government funding at time \(t = 0\))
- \(f(8) = 1.3\) (government funding at time \(t = 8\))

Substituting the values:

\[
\text{Average Rate of Change} = \frac{1.3 - 1.5}{8 - 0} = \frac{-0.2}{8} = -0.025
\]

Now, to express this to two significant figures:

\[
-0.025 \approx -0.025 \text{ (to two significant figures)}
\]

The units of measurement are in units of funding per unit of time (e.g., million dollars per year).

Thus, the average rate of change of government funding for the arts over the period \([0, 8]\) is approximately \(-0.025\) units of funding per year.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. How would the average rate of change differ if \(f(8)\) were 1.7 instead of 1.3?
2. What is the significance of the negative sign in the average rate of change?
3. Can the average rate of change be interpreted as a slope? If so, how?
4. How would you calculate the average rate of change over a non-uniform interval, say from \(t = 2\) to \(t = 5\)?
5. How does the average rate of change relate to instantaneous rates of change in calculus?

**Tip:** Remember that the average rate of change can be interpreted as the slope of the secant line connecting two points on a function.

Learn how to estimate the average rate of change of government funding for the arts over a specified period. Use the given function values at the start and end of the interval, applying the average rate of change formula. Includes an example calculation and interpretation.

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