Answer:
The rate of change of elevation tends to a constant value.
Explanation:
The average rate of change of e(x) on the interval [a, b] defined as
[tex]m_{\text{avg}}=\frac{e(b)-e(a)}{b-a}[/tex]
which explicitly we can write as
[tex]m_{\text{avg}}=\frac{\sqrt[]{b-10}-\sqrt[]{a-10}}{b-a}[/tex]
Now, the question is, what happens to m_avg as we increase b while keeping a fixed?
As b becomes large then √b -10 becomes √b and b - a becomes b (since a is comparatively small); therefore, m_avg becomes
[tex]m_{\text{avg}}=\frac{\sqrt[]{b-10}-\sqrt[]{a-10}}{b-a}\Rightarrow\frac{\sqrt[]{b}-\sqrt[]{a-10}}{b}\Rightarrow\frac{\sqrt[]{b}}{b}[/tex][tex]\Rightarrow m_{\text{avg}}=\frac{\sqrt[]{b}}{b}[/tex]
which for any fixed value of b is a constant.
The same behaviour can be extrapolated by looking at the graph of e(x).
As can be seen from the graph, as x increases, the slope of the function becomes flatter and flatter, meaning it tends to be a constant. In other words, for large values of x, you can approximate the slope of the function by a straight line.
