Answered: Compute the average rate of change of f…

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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Increasing numbers of manatees ("sea sirens") have been killed by boats off the Florida coast. The following graph shows the relationship between the number of boats registered in Florida 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 approximate point (4.5, 16.99), passes through the point (5, 18.75), passes through the point (6, 27.6), passes through the point (7, 43.55), passes through the point (8, 66.6), passes through the approximate point (8.5, 80.79), and exits the window in the first quadrant.

The regression curve shown is given by

f(x) = 3.55x² − 30.2x + 81 manatees (4.5 ≤ x ≤ 8.5),

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

(a)

Compute the average rate of change of f over the intervals [5, 6] and [7, 8].

rate of change over [5, 6] = manatee deaths per 100,000 boats rate of change over [7, 8] = manatee deaths per 100,000 boats

(b)

What does the answer to part (a) tell you about the manatee deaths per boat?

More boats result in more manatee deaths per additional boat.Less boats result in more manatee deaths per additional boat. More boats result in less manatee deaths per additional boat.

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