Explanation Theorem used: If | r | < 1 , then the geometric series ∑ n = 0 ∞ a r n = a + a r + a r 2 + ⋯ converges and it sum is a 1 − r ; that is, ∑ n = 0 ∞ a r n = a + a r + a r 2 + ⋯ = a 1 − r . The series diverges if | r | ≥ 1 . Calculation: It is given that the total number of individuals S n , who have contracted the disease some time between the first and n th day is approximated by S n = a 1 + a N a 1 + a N a 2 + ⋯ + a N a n − 1 . Consider a n + 1 = ( 1 + a N − b ) a n . Let r = 1 + a N − b such that a n + 1 = r a n . Thus, a n + 1 = r a n = r 2 a n − 1 = r n a 1 , a n = r n − 1 a 1 , a 2 = r a 1 , a 3 = r 2 a 1 and so on. Substitute the above values in S n = a 1 + a N a 1 + a N a 2 + ⋯ + a N a n − 1

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 11.3, Problem 39E

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To show: If r<1, where r=1+aN−b, then the total number of persons who will have contracted the disease at some stage of the epidemic is no larger than a1b(b−aN).

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Chapter 11.3, Problem 38E

Chapter 11.3, Problem 40E

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Chapter 11 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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If r < 1 , where r = 1 + a N − b , then the total number of persons who will have contracted the disease at some stage of the epidemic is no larger than a 1 b ( b − a N ) .

Solution Summary: The author calculates that the total number of persons who contracted the disease at some stage of the epidemic is no larger than a_1b(b-aN).

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To show: If r<1, where r=1+aN−b, then the total number of persons who will have contracted the disease at some stage of the epidemic is no larger than a1b(b−aN).

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Chapter 11 Solutions

If r &lt; 1 , where r = 1 + a N − b , then the total number of persons who will have contracted the disease at some stage of the epidemic is no larger than a 1 b ( b − a N ) .

Solution Summary: The author calculates that the total number of persons who contracted the disease at some stage of the epidemic is no larger than a_1b(b-aN).

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To show: If r<1, where r=1+aN−b, then the total number of persons who will have contracted the disease at some stage of the epidemic is no larger than a1b(b−aN).

Want to see the full answer?

Chapter 11 Solutions

If r < 1 , where r = 1 + a N − b , then the total number of persons who will have contracted the disease at some stage of the epidemic is no larger than a 1 b ( b − a N ) .