Suppose that \(C(2000) = 800\) and \(C'(2000) = 0.35\text{.}\) Estimate \(C(2100)\text{,}\) and justify your estimate by writing at least one sentence that explains your thinking.
Suppose someone claims that \(C'(5000) = -0.1\text{.}\) What would the practical meaning of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?
