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# Applied Math 40S June 6, 2008

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Fractal and sequences applications.

Fractal and sequences applications.

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### Transcript

• 1. Fractals are everywhere in the world around us, even in our bodies ... A fractal fern leaf by ﬂickr user Paulo Henrique Zioli
• 2. TED Talks Ron Eglash: African fractals, in buildings and braids http://www.ted.com/index.php/talks/view/id/198
• 3. The Rectangle ... Draw a rectangle that measures 12 cm by 8 cm, and shade the inside of the rectangle. Construct the midpoints of each side of the rectangle, and then draw a quadrilateral by joining these points. Shade the quadrilateral white. Now continue the process by finding the midpoints of the quadrilateral, drawing the rectangle, and shading it the same colour as the first rectangle. Draw six generations. (The initial rectangle is the first generation.) (a) Find the total shaded area. (b) Find the total unshaded area.
• 4. The Rectangle ... (b) Find the total unshaded area. (a) Find the total shaded area.
• 5. The Square ... Create a fractal that begins with a large square 20 cm on each side. Each pattern requires that the square be divided into four equally sized squares, that the bottom-left square be shaded, and the process continues in the upper-right square. Repeat the process four times. (a) Find the total shaded area. (b) Find the total unshaded area.
• 6. The Square ... (b) Find the total unshaded area. (a) Find the total shaded area.
• 7. A Fractal: The Koch Snowflake All about the Koch Snowflake on wikipedia
• 8. The total perimeter of iteration 3, to the nearest centimetre, will be ________. The total perimeter of iteration 13, to the nearest centimetre, will be ________.
• 9. People on Mars A group of 100 astronauts is sent to Mars to colonize the planet. NASA scientists have predicted that the population will increase by 12 percent every 20 years. Find the terms of the sequence for the first 100 years. (a) Write a recursive formula for this sequence. (b) Draw a graph of the sequence of populations over 100 years. Describe the shape of the graph. (c) Draw a graph of the sequence of populations over 300 years. Does the graph still look the same as it did before?
• 10. Level of Medication Anthony, a worker in a medical lab, has accidentally been exposed to bacteria that cause the disease anthrax. The treatment he uses is the antibiotic Cipro, which he must take every 12 hours. His body eliminates 75 percent of the medication in 12 hours. The level of medication in his body should be around 24 mg, and never higher than 36 mg. How many milligrams of Cipro should he take to maintain the proper level of medication in his body?