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31. Bird Flight A bird is released from point A on an island, 5 mi from the nearest point B on 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 and 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) = 14VX² + 25 + 10(12 – x) (b) If the bird instinctively chooses a path that minimizes its energy expenditure, to what point does it fly? island [5 mi D nesting area 12 mi

31. Bird Flight A bird is released from point A on an island, 5 mi from the nearest point B on 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 and 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) = 14VX² + 25 + 10(12 – x) (b) If the bird instinctively chooses a path that minimizes its energy expenditure, to what point does it fly? island [5 mi D nesting area 12 mi

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 51E
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In the problem you are asked to find a function that models a real life-life situation and then use the model to answer questions about the situation. 

 

31. Bird Flight A bird is released from point A on an island, 5 mi from the nearest point B on 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 and 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) = 14VX² + 25 + 10(12 – x) (b) If the bird instinctively chooses a path that minimizes its energy expenditure, to what point does it fly? island [5 mi D nesting area 12 mi
Transcribed Image Text:31. Bird Flight A bird is released from point A on an island, 5 mi from the nearest point B on 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 and 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) = 14VX² + 25 + 10(12 – x) (b) If the bird instinctively chooses a path that minimizes its energy expenditure, to what point does it fly? island [5 mi D nesting area 12 mi
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