Captain Picard and the rest of the crew of the Enterprise are defending their position on the moon Yavin IV against the evil robotic Cylon invaders. Each day of the battle, 1500 Cylons arrive at dawn, and throughout the day the crew is able to eliminate 70% 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 formula for the number of Cylons at the end of the day on the nth day of the battle. (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 force of 2000 soldiers, how many should they send each day?