Chapter 2, Problem 31P

In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you.

Bird Flight A bird is released from point A on an island. 5 mi from the nearest point Bon a straight shoreline. The bird flies to a point C on the shoreline and then flies along the shoreline to its nesting area D (see the figure). Suppose the bird requires 10 Kcal/mi of energy to fly over land md 14 kcal/mi to fly over water.
a) Use the fact that

energy used = energy per mile X miles flown
to show that the total energy used by the bird is modeled by the function

$E(x)=14\sqrt{x^2+25}+10(12-x)$
(b) If the bird instinctively chooses a path that minimizes its energy expenditure, to whatpoint does it fly?