# ALGEBRA (rational exponents, radical expressions)

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 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 thousandths 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.