Graphing Exponential Growth

This lesson explains how to graph a basic exponential function using paper folding as a model. It covers the concept of exponential growth, where the number of paper layers doubles with each fold, and demonstrates how to graph these functions, highlighting the horizontal asymptote and the behavior of the graph as X approaches negative infinity. The lesson also addresses common misconceptions about vertical asymptotes and emphasizes the domain of exponential functions.

What is the base condition for an exponential growth function?

• The base must be a fraction.

• The base must be zero.

• The base must be a positive real number greater than one.

• The base must be a negative number.

How many layers of paper are there after two folds?

• Sixteen layers

• Eight layers

• Four layers

• Two layers

What is the exponential function that models the number of paper layers after X folds?

• y = 2^X

• y = X^2

• y = X/2

• y = 2X

What happens to the value of Y as X approaches negative infinity in an exponential function?

• Y approaches infinity

• Y remains constant

• Y approaches zero

• Y becomes negative

What is the Y-intercept of the exponential function y = 2^X?

• (0, 0)

• (0, 1)

• (1, 0)

• (1, 1)

What is a common misconception about the graph of exponential growth functions?

• They have a horizontal asymptote.

• They have a vertical asymptote.

• They are linear.

• They decrease over time.

What is the domain of the exponential function y = 2^X?

• All positive numbers

• All negative numbers

• All real numbers

• Only integers