Learning Resources
Home » » Courses » Mathematics » Advanced Mathematics 3205 (delisted) » Unit 03 » Set 01 ILO 01 » Get Ready
Outcomes
In this lesson you will
- review how real-world relationships can be modeled using graphs
- explore the common properties of geometric sequences, including the calculation of the common ratio
- explore the properties of number patterns that grow exponentially
By the end of this section students will be able to:
- model real-world phenomena using exponential functions
- sketch graphs from descriptions, tables, and collected 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 of real numbers in exponential and logarithmic expressions and equations
- apply real number exponents in expressions and equations
Introduction
Mathematical Modeling, Book 3 p.108 - 126
This section starts with a review of matching situations to graphs. The exponential function 
where b > 1( the growth curve) and b < 1 (the decay curve) is introduced in terms of modeling a real situation. You will find that there is a common ratio between successive y-values if the x-values are changing by the same amount for exponential functions of this form. The emphasis will be on using tables and graphs to find the relationships that exist for the exponential function.
This section should take 5 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- use graphs to model descriptions of real-world situations
- number patterns that are not arithmetic
- graphing technology and spreadsheet software