7. (Wood Pile) A ship crew trapped on an island builds a signal fire to alert passing ships. They...
7. (Wood Pile) A ship crew trapped on an island builds a signal fire to alert passing ships. They start the fire with 200 pounds of wood. During the course of the day, 60% of the wood pile burns away. At the end of each day, they add another 200 pounds of wood to the pile. Let W, denote the weight of the wood pile in pounds immediately after adding the ith load of wood, where W-200. (a) Find an expression for Wn that does not contain a large summation. (b) Instead of starting with 200 pounds of wood and adding 200 pounds every day, they start with P pounds of wood and add P pounds every day. If they plan to continue the fire indefinitely determine the largest value of P for which the weight of the wood pile will never exceed 1000 pounds
7. (Wood Pile) A ship crew trapped on an island builds a signal fire to alert passing ships. They start the fire with 200 pounds of wood. During the course of the day, 60% of the wood pile burns away. At the end of each day, they add another 200 pounds of wood to the pile. Let W, denote the weight of the wood pile in pounds immediately after adding the ith load of wood, where W-200. (a) Find an expression for Wn that does not contain a large summation. (b) Instead of starting with 200 pounds of wood and adding 200 pounds every day, they start with P pounds of wood and add P pounds every day. If they plan to continue the fire indefinitely determine the largest value of P for which the weight of the wood pile will never exceed 1000 pounds