Question 3 Captain Picard and the rest of the crew of the Rocinante are defending their position on Tatooine against the evil robotic Cylon invaders. Each day of the battle, 1500 Cylons arrive at dawn, and throughout each day the crew is able to eliminate 60% of the Cylons on the battlefield. (a) Let Cn be the number of Cylons on the planet at the end of the day on the nth day of the battle. Find C1, C2, and C3. (b) Find an explicit, closed-form formula for the number of Cylons at the end of the day on the nth day of the battle. (Explicit means we write C, as a function of n alone as opposed to a recursive formula where Cn is written in terms of Cn-1. By closed-form, we mean a formula without shorthand such as sigma notation or + . +.) (c) In the long run, how many Cylons will be on the planet after a day of battle? (d) If instead the Cylons want to maintain a minimum force of 5000 soldiers, how many should they send each day?

Question 3 Captain Picard and the rest of the crew of the Rocinante are defending their position on Tatooine against the evil robotic Cylon invaders. Each day of the battle, 1500 Cylons arrive at dawn, and throughout each day the crew is able to eliminate 60% of the Cylons on the battlefield. (a) Let Cn be the number of Cylons on the planet at the end of the day on the nth day of the battle. Find C1, C2, and C3. (b) Find an explicit, closed-form formula for the number of Cylons at the end of the day on the nth day of the battle. (Explicit means we write C, as a function of n alone as opposed to a recursive formula where Cn is written in terms of Cn-1. By closed-form, we mean a formula without shorthand such as sigma notation or + . +.) (c) In the long run, how many Cylons will be on the planet after a day of battle? (d) If instead the Cylons want to maintain a minimum force of 5000 soldiers, how many should they send each day?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

ChapterP: Prerequisites

SectionP.3: Integer Exponents And Scientific Notation

Problem 56E: Discuss how big is a billion? If you had a million (106) dollars in a suitcase and you spend $1000...

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