Explanation Given information: The Ricker equation: x t + 1 = c x t e − x t was introduced in Exercise 1.6.32. x 0 = 0.2 , c = 2 Calculation: Given difference equation x t + 1 = c x t e − x t Where x 0 = 0.2 , c = 2 , Let us calculate some terms of the sequence. x 0 = 0.2 x 1 = 2 x 0 e − x 0 = 2 ( 0.2 ) e − 0.2 ≈ 0.3275 x 2 = 2 x 1 e − x 1 ≈ 2 ( 0.3275 ) e − 0.3275 = 0.4721 x 3 = 2 x 2 e − x 2 ≈ 2 ( 0.4721 ) e − 0.4721 ≈ 0.5889 x 4 = 2 x 3 e − x 3 ≈ 2 ( 0.5889 ) e − 0.5889 ≈ 0.6536 x 5 = 2 x 4 e − x 4 ≈ 2 ( 0.6536 ) e − 0.6536 ≈ 0.6800 x 6 = 2 x 5 e − x 5 ≈ 2 ( 0.6800 ) e − 0.6800 ≈ 0.6900 x 7 = 2 x 6 e − x 6 ≈ 2 ( 0.6900 ) e − 0.6900 ≈ 0.6918 x 8 = 2 x 7 e − x 7 ≈ 2 ( 0.6918 ) e − 0

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 2.1, Problem 55E

To determine

To plot: enough terms of the Ricker equation to see how the terms behave and estimate the limit and then, assuming the limit exists, calculate its exact value. If not, describe the behavior of the terms

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Chapter 2.1, Problem 54E

Chapter 2.1, Problem 56E

Chapter 2 Solutions

Biocalculus

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Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?
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