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Pre-Cal 40S Slides January 22, 2008

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Review of Geometric Sequences and Exam review.

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Pre-Cal 40S Slides January 22, 2008

1. 1. Sequences Review Like all of mathematics, it's really just a search for patterns in the world around us ... The Dream of Prometheus
2. 2. Given a geometric sequence with = 12 and = 4, find .
3. 3. Suppose that a golf ball, when dropped on a floor, rebounds 2/3 of the distance from which it is dropped. For example, if the ball is dropped from 6 feet, the ball will bounce upwards 4 feet. (a) What is the total distance that the golf ball rebounds if you drop it from 6 feet, and watch it rebound successively 4 times? (b) What is the total distance that the golf ball rebounds if you drop it from 6 feet, and watch it rebound successively until it comes to a stop?
4. 4. (a) Explain why {8,4,2,0} cannot be the first 4 terms of an arithmetic sequence. (b) Show how you can make {8,4,2,0} into the first four terms of an arithmetic sequence by changing only one term. (c) Show how you can make {8,4,2,0} into the first four terms of a geometric sequence by changing only one term.
5. 5. The sum of the terms in an infinite geometric series is 4 and the common ratio is . Find the first term.
6. 6. If a sheet of paper 0.002 cm thick is torn in half 50 times , with all the pieces piled on top of each other prior to each tear, how thick is the stack of paper to the nearest km? Read about Britney Gallivan
7. 7. The enrollment at DMCI was 400 in 1973. If the school’s population has increased 5% a year, how many students will be going to DMCI in 2010?
8. 8. The fractal shown in the diagram below is created as follows: • A shaded triangle is formed by joining the midpoints of the vertical and horizontal sides. • A vertical line is drawn from the midpoint of the horizontal side, creating a new isosceles right triangle. • The process is continued. Find the total shaded area. Original 1st Iteration 2nd Iteration
9. 9. A Fractal: The Koch Snowflake All about the Koch Snowflake on wikipedia
10. 10. Two species of ants, the red ants and black ants, are preparing for battle. Each day the number of red ants increases by 2%, while the number of black ants increases by 2000 per day. Initially (day 1) each side has 1000 ants. (a) Find an explicit formula for the number of black ants on day n. (b) Find an explicit formula for the number of red ants on day n. (c) On day 365 which species has the larger population?