Answered: cology Increasing numbers of manatees…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Ecology Increasing numbers of manatees have been killed by boats off a state's coast. The following graph shows the relationship between the number of boats registered in that state and the number of manatees killed each year.

The graph has horizontal axis labeled "Boats (100,000)" and vertical axis labeled "Manatee deaths." The graph has a scatter plot of 24 points and a regression curve through the points. The regression curve enters the window in the first quadrant, goes up and right becoming more steep, passes through the point (4.5, 16.38), passes through the point (5, 18), passes through the point (6, 26.52), passes through the point (7, 42.08), passes through the point (8, 64.68), passes through the point (8.5, 78.62), and exits the window in the first quadrant.

The regression curve shown is given by

f(x) = 3.52x² − 30.2x + 81 manatee deaths (4.5 ≤ x ≤ 8.5),

where x is the number of boats (hundreds of thousands) registered in the state in a particular year and f(x) is the number of manatees killed by boats in the state that year.

Compute f ′(8).

f ′(8) = matinee deaths per 100,000 additional boats

Interpret your answer.

At a level of 800,000 boats, the number of manatee deaths was increasing at a rate of per 100,000 additional boats.

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