Exponential Functions and Growth Patterns

This lesson covers how to write and graph exponential functions by examining real-life scenarios. It begins with an introduction to exponential functions, highlighting their characteristics and common mistakes. The lesson then explores two examples: modeling bacteria population growth and the exponential decay of a bouncing baseball. Each example includes writing equations, creating tables, and graphing the functions. The lesson concludes by summarizing the key points about exponential relationships.

What is the general form of an exponential function?

• f(x) = a/b^x

• f(x) = ax^b

• f(x) = a * b^x

• f(x) = a + bx

Which of the following is a common mistake when writing exponential functions?

• Using the variable as the base

• Using the common ratio as the base

• Using the initial amount as the exponent

• Using the common ratio as the exponent

In the bacteria population example, what is the initial amount of bacteria?

• 50 bacteria

• 200 bacteria

• 100 bacteria

• 150 bacteria

What is the common ratio in the bacteria population example?

• 2

• 0.5

• 1

• 3

How does the population change every hour in the bacteria example?

• It halves

• It triples

• It doubles

• It remains constant

What is the initial height of the baseball in the exponential decay example?

• 60 inches

• 52 inches

• 45 inches

• 30 inches

What percentage of its height does the baseball retain after each bounce?

• 25%

• 10%

• 50%

• 75%

What is the common ratio in the baseball bounce example?

• 0.5

• 0.75

• 0.25

• 0.1

What type of exponential function is demonstrated by the baseball bounce example?

• Exponential decay

• Linear growth

• Linear decay

• Exponential growth

What do the equation, table, and graph represent in both examples?

• Linear relationships

• Different relationships

• The same exponential relationship

• Unrelated concepts