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Unit 3 Discussion will focus on learning about rational exponents and radical expressions. During the Discussion activity, you will be choosing from a couple of interesting applications and then sharing your work and findings with the class to learn how these skills can be applied in real life.
There are three parts to the Unit 3 Discussion activity. Be sure to complete all three components to earn the most points! Click on the Discussion link located below the unit button to the left for full details and instructions.
Rational Exponents and Radical Expressions
Swing or Drink?
Part 1: Choose one of the following to complete.
Pendulum: A circus trapeze can be thought of a pendulum because it swings back and forth in the same way. The formula for the time it takes for a pendulum, or trapeze artist, to make one full swing (the period) can be calculated using the following formula:
T is time to complete one full swing (period) in seconds, L is the length of the pendulum in feet, and g is the acceleration of gravity, 32 ft./s^{2}. Use 3.14 for π. Round all other numbers to the thousandths place. Using your height in feet for L, the length of the pendulum, how long would it take to make one full swing on the pendulum? Share your height and calculations with the class.
Half-life: The half-life of caffeine is found using the formula:
A is the amount of caffeine left in your body after two hours, C is the amount of caffeine originally ingested, and k is the half-life of caffeine (about 5.7 hours). Round all other numbers to the thousandth place. Find the amount of caffeine in your favorite caffeinated beverage by checking the nutrition label or doing research on the internet. Be sure to find the amount of caffeine in the entire container, not just in one serving. This will be C in the equation. Assume you drink the entire beverage in one sitting. Share the name of your favorite caffeinated beverage, the amount of caffeine in the beverage, and your calculations for how much caffeine will be left in your system after 2 hours with the class.Click here to see an example.
Part 2:
Complete one of the following:
If you worked a Pendulum problem, select a classmate who chose the Half-Life problem. How much caffeine would be left in their system after 2 hours if they completely drank 3 beverages in one sitting? Show all of your calculations. Compare your answer with the original answer calculated by your classmate. Does the difference in answers make sense? Why or why not?
If you worked a Half-Life problem, select a classmate who chose the Pendulum problem. If another member of the circus lengthened the trapeze by one foot, how long would it take the trapeze artist to complete one full swing with their new length? Show all of your calculations. Compare your answer with the original answer calculated by your classmate. Does the difference in your calculations make sense? Why or why not?
Part 3:
Find and comment on at least one classmate’s post for Part 1 or Part 2. Make sure your comments are substantive and advance the Discussion. If their answer is not correct, tactfully identify the error and show the work correctly. Share any appropriate and interesting scenarios that may explain the change in length of the trapeze or the decision to triple their caffeine intake in Part 2. Humor and creativity are encouraged.
Note:
Your responses to your classmates must be substantive and advance the Discussion. Substantive means your reply must 1) include comments specific to that particular post and 2) contain information or insight worthy of sharing with the instructor and class. Contact your instructor if you have questions about making substantive responses. MM212 College Algebra Unit 3 Discussion