To solve the problem, we need to compare the average rate of change from [tex]\( x=0 \)[/tex] to [tex]\( x=15 \)[/tex] with the average rate of change from [tex]\( x=0 \)[/tex] to [tex]\( x=20 \)[/tex].
Here’s the step-by-step explanation:
1. Understand the Given Information:
- We are provided with the average rate of change from [tex]\( x=0 \)[/tex] to [tex]\( x=15 \)[/tex], which is [tex]\(-4.667\)[/tex].
2. Define Average Rate of Change:
- The average rate of change of a function [tex]\( f \)[/tex] over an interval [tex]\([a, b]\)[/tex] is given by:
[tex]\[
\frac{f(b) - f(a)}{b - a}
\][/tex]
This means we observe how the function values change between [tex]\( x=a \)[/tex] and [tex]\( x=b \)[/tex].
3. Comparison Insight:
- To compare the average rate of change from [tex]\( x=0 \)[/tex] to [tex]\( x=20 \)[/tex] with the given rate from [tex]\( x=0 \)[/tex] to [tex]\( x=15 \)[/tex], we examine whether the trend continues linearly or changes.
4. Interpretation:
- If it's specified that the average rate of change from [tex]\( x=0 \)[/tex] to [tex]\( x=20 \)[/tex] is "decreasing", it implies that the rate of change has become more negative or less positive between [tex]\( x=0 \)[/tex] and [tex]\( x=20 \)[/tex] compared to [tex]\( x=0 \)[/tex] to [tex]\( x=15 \)[/tex].
5. Conclusion:
- In this context, the average rate of change from [tex]\( x=0 \)[/tex] to [tex]\( x=20 \)[/tex] compared to [tex]\( x=0 \)[/tex] to [tex]\( x=15 \)[/tex] is indeed:
[tex]\[
\text{The average rate of change from } x=0 \text{ to } x=20 \text{ is decreasing compared to the average rate of change from } x=0 \text{ to } x=15.
\][/tex]
Thus, we conclude:
[tex]\[
\boxed{\text{decreasing}}
\][/tex]
