Learning Resources

Outcomes

In this lesson you will

• Review how real-world relationships can be modeled using graphs.
• Explore the properties of number patterns that grow exponentially.

By the end of this section you should be able to:

• Model real world phenomena using exponential growth.
• Sketch graphs from descriptions, tables, and collect data.
• Demonstrate an intuitive understanding of the recursive nature of exponential growth.
• Demonstrate an understanding of patterns that are arithmetic, power, and geometric, and relate them to corresponding functions.
• Analyze tables and graphs to distinguish between linear, quadratic, and exponential relationships.
• Describe and interpret domains and ranges using set notation.
• Analyze and describe the characteristics of exponential and logarithmic functions.
• Demonstrate an Understanding of the role or real numbers in exponential and logarithmic expressions and equations.
• Apply real number exponents in expressions and equations.

Introduction

In this section you will review how to use graphs to model real-world relationships. You will be introduced to exponential functions of the form , where, (this is the growth curve) and (this is the decay curve).

You will also discover in this section that there is a common ratio between successive y-values if the x-values are changing by the same amounts for exponential functions of this form.

This section should take you between 5 & 6 hours to complete.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• How to analyze graphs to gain specific information.
• How to work with powers.