Explanation Given: The number N of civilizations per galaxy that might be able to communicate with us can be expressed in the formula, N = S P Z B I L . Here S is the number of stars per galaxy, about 2 × 10 11 . The remaining variables, together with their pessimistic and optimistic estimates are given in the following table, Variable Meaning Pessimistic value Optimistic value P Fraction of stars with planets 0.01 1 Z Planets per star in life zone for atleast 4 billion years 0.01 1 B Fraction of suitable planets on which life begins 0.01 1 I Fraction of life forms that evolve to intelligence 0.01 1 L Fraction of star’s life during which a technological society survives. 10 − 8 10 − 4 Calculation: For finding the most pessimistic value of N , substitute S = 2 × 10 11 , Z = 0.01 , B = 0.01 , I = 0.01 a n d L = 10 − 8 in the equation given below, N = S P Z B I L N = ( 2 × 10 11 ) ( 0.01 ) ( 0.01 ) ( 0.01 ) ( 0.01 ) ( 10 − 8 ) N = ( 2 × 10 11 ) ( 0.00000001 ) × 10 − 8 N = 2 × 10 11 × 0 To determine (b) To calculate: The value of L will give 1 communicating civilization per galaxy using pessimistic estimates for other variables when the pessimistic estimate corresponds to 100 years, the optimistic estimate to 1,000,000 years. To determine (c) To explain: Whether this formula helpful in determining whether there is life on other planets

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

6th Edition

ISBN: 9781337111348

Author: Bruce Crauder, Benny Evans, Alan Noell

Publisher: Cengage Learning

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Chapter 3.2, Problem 29E

To determine

(a)

To calculate:

The most pessimistic and most optimistic values for N

To determine

(b)

To calculate:

The value of L will give 1 communicating civilization per galaxy using pessimistic estimates for other variables when the pessimistic estimate corresponds to 100 years, the optimistic estimate to 1,000,000 years.

To determine

(c)

To explain:

Whether this formula helpful in determining whether there is life on other planets

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Chapter 3.2, Problem 28E

Chapter 3.2, Problem 1SBE

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

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(a) To calculate: The most pessimistic and most optimistic values for N

Solution Summary: The author calculates the most pessimistic and most optimistic values for N using the formula, N=SPZBIL.

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(a) To calculate: The most pessimistic and most optimistic values for N

(b) To calculate: The value of L will give 1 communicating civilization per galaxy using pessimistic estimates for other variables when the pessimistic estimate corresponds to 100 years, the optimistic estimate to 1,000,000 years.

(c) To explain: Whether this formula helpful in determining whether there is life on other planets

Want to see the full answer?

Chapter 3 Solutions

(a)

To calculate:

The most pessimistic and most optimistic values for N

(b)

To calculate:

The value of L will give 1 communicating civilization per galaxy using pessimistic estimates for other variables when the pessimistic estimate corresponds to 100 years, the optimistic estimate to 1,000,000 years.

(c)

To explain:

Whether this formula helpful in determining whether there is life on other planets