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82 CHAPTER 2 Limits and Derivatives 2.1 EXERCISES 1. A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. acibhn t (min) 10 15 20 25 30 V (gal) 694 444 250 111 28 0. (a) If P is the point (15, 250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t = 5, 10, 20, 25, and 30. (b) Estimate the slope of the tangent line at P by averaging %3D the slopes of two secant lines. (c) Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.) A cardiac monitor is used to measure the heart rate of a patient It compiles the number of heartbeats after t min- after surgery. utes. When the data in the table are graphed, the slono tangent

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.4: Solving Nonlinear Equations

Problem 21E: Grazing Kangaroos The amount of vegetation eaten in a day by a grazing animal V of food available...

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I need help with a-c please.

82
CHAPTER 2 Limits and Derivatives
2.1 EXERCISES
1. A tank holds 1000 gallons of water, which drains from the
bottom of the tank in half an hour. The values in the table
show the volume V of water remaining in the tank (in gallons)
after t minutes.
acibhn
t (min)
10
15
20
25
30
V (gal)
694
444
250
111
28
0.
(a) If P is the point (15, 250) on the graph of V, find the
slopes of the secant lines PQ when Q is the point on the
graph with t = 5, 10, 20, 25, and 30.
(b) Estimate the slope of the tangent line at P by averaging
%3D
the slopes of two secant lines.
(c) Use a graph of the function to estimate the slope of the
tangent line at P. (This slope represents the rate at which
the water is flowing from the tank after 15 minutes.)
A cardiac monitor is used to measure the heart rate of a
patient
It compiles the number of heartbeats after t min-
after
surgery.
utes. When the data in the table are graphed, the slono
tangent

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Grazing Kangaroos The amount of vegetation eaten in a day by a grazing animal V of food available measured as biomass, in units such as pounds per acre. This relationship is called the functional response. If there is little vegetation available, the daily intake will be small, since the animal will have difficulty finding and eating the food. As the amount of food biomass increases, so does the daily intake. Clearly, though, there is a limit to the amount the animal will eat, regardless of the amount of food available. This maximum amount eaten is the satiation level. a.For the western grey kangaroo of Australia, the functional response is G=2.54.8e0.004V, where G=G(V) is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Draw a graph of G against V. Include vegetation biomass levels up to 2000 pounds per acre. ii. Is the graph you found in part i concave up or concave down? Explain in practical terms what your answer means about how this kangaroo feeds. iii. There is a minimal vegetation biomass level below which the western grey kangaroo will eat nothing. Another way of expressing this is to say that the animal cannot reduce the food biomass below this level. Find this minimal level. iv. Find the satiation level for the western grey kangaroo. b. For the red kangaroo of Australia, the functional response is R=1.91.9e0.033V, Where R is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Add the graph of R against V to the graph of G you drew in part a. ii. A simple measure of the grazing efficiency of an animal involves the minimal vegetation biomass level described above: The lower the minimal level for an animal, the more efficient it is at grazing. Which is more efficient at grazing, the western grey kangaroo or the red kangaroo?

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