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(d) If instead the Cylons want to maintain a minimum force of 5000 soldiers, how many should they send each day?

(d) If instead the Cylons want to maintain a minimum force of 5000 soldiers, how many should they send each day?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 38E
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part d please

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 C, 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 Cp-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?
Transcribed Image Text: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 C, 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 Cp-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?
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