Understanding Exponential Growth & Decay in Texas Algebra I Lesson 47

1. Texas Algebra I Lesson 47: Exponents, Exponential Growth and Decay

2. Lesson Objectives The student will be able to: • Define exponential growth and decay • Define growth factor, decay factor • Identify situations where exponential growth and decay apply

3. Exponential Growth Exponential growth describes situations that grow consistently, but the numbers get much larger in a small amount of time. Some examples of these are population and bacterial growth and compound interest.

4. Exponential Growth Can be modeled by the function: a is the starting amount, b is the rate of change, and x is the number of years. The base, b, is called the growth factor. Ex. Since the year 2000, Florida’s population has grown consistently at a rate of 2% per year. What is the population in 2012 if the population in 2000 was 15.9 million?

5. Exponential Decay As you can imagine, exponential decay is when a population or amount decreases rather than increases. It can be modeled with the function: a is the starting amount, b is the rate of change, and x is the number of years. The base, b, is called the decay factor. In 1980 the average person drank 16.5 gallons of milk per year. If the consumption of milk by Americans has dropped 4.1% per year, how much milk was consumed per person in 2002?

6. Lesson Objectives The student will be able to: • Define exponential growth and decay • Define growth factor, decay factor • Identify situations where exponential growth and decay apply