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1.2. A population is assumed to be governed by the equation Nn+1 = f(Nn), where the function f is as shown in Figure 1.5, and there is a single steady state N*. A variant of the cobwebbing method uses the graphs off and its reflection f to produce successive iterates Nn, as in part (a) of the figure. %3D a) What is the point marked S in part (a) of the figure? b) A somewhat different situation is shown in part (b) of the figure. Interpret the points A, B and C and use cobwebbing to decide what happens to the population Nn. (a) (b) 2 2 x=f(y) y=x y=x 1.5 1.5 y=f(x) 1 > 1 y=f(x) x=f(y) 0.5 0.5 B 0.5 1 1.5 2 0.5 1 1.5 2

1.2. A population is assumed to be governed by the equation Nn+1 = f(Nn), where the function f is as shown in Figure 1.5, and there is a single steady state N*. A variant of the cobwebbing method uses the graphs off and its reflection f to produce successive iterates Nn, as in part (a) of the figure. %3D a) What is the point marked S in part (a) of the figure? b) A somewhat different situation is shown in part (b) of the figure. Interpret the points A, B and C and use cobwebbing to decide what happens to the population Nn. (a) (b) 2 2 x=f(y) y=x y=x 1.5 1.5 y=f(x) 1 > 1 y=f(x) x=f(y) 0.5 0.5 B 0.5 1 1.5 2 0.5 1 1.5 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 47RE
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1.2. A population is assumed to be governed by the equation Nn+1 = f(Nn), where the function f is as shown in Figure 1.5, and there is a single steady state N*. A variant of the cobwebbing method uses the graphs of f and its reflection f to produce successive iterates Nn, as in part (a) of the figure. a) What is the point marked S in part (a) of the figure? b) A somewhat different situation is shown in part (b) of the figure. Interpret the points A, B and C and use cobwebbing to decide what happens to the population Nn. (a) (b) x=f(y)/ y=x y=x 1.5 1.5 y=f(x) 1 > 1 y=t(x) x=f(y) 0.5 0.5 B 0.5 1 1.5 0.5 1 1.5 2
Transcribed Image Text:1.2. A population is assumed to be governed by the equation Nn+1 = f(Nn), where the function f is as shown in Figure 1.5, and there is a single steady state N*. A variant of the cobwebbing method uses the graphs of f and its reflection f to produce successive iterates Nn, as in part (a) of the figure. a) What is the point marked S in part (a) of the figure? b) A somewhat different situation is shown in part (b) of the figure. Interpret the points A, B and C and use cobwebbing to decide what happens to the population Nn. (a) (b) x=f(y)/ y=x y=x 1.5 1.5 y=f(x) 1 > 1 y=t(x) x=f(y) 0.5 0.5 B 0.5 1 1.5 0.5 1 1.5 2
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