Purpose: This section will introduce students to exponential growth in a situation the students can model. They will be exposed to the motivation behind the notation for exponents and their meaning. They will also beging to look at the form of a function that represents a situation involving repeated multiplication (in this case doubling).

Purpose: Students will explore what happens when there are different growth factors. The students will have to use properties of exponents and should develop a foundation for understanding fractionaly exponents.

Purpose: Students will get to explore a situation in which there is both a constant rate of change and a constant percentage change. They will explore the similarities and differences in the growth patterns. This will help students understand the difference between the two types of growth as well as understand how a growth factor works.

Purpose: The students will become familiar with the notion of repeated multiplication for various time intervals. Also they will become comfortable with expressing exponents as rational numbers.

Purpose: This section will allow students to explore what happens when there are additional compounding periods and how it affects the basic investment formula. They will get to create the general investment formula and determine growth factors for various compounding periods. This section will also serve as a lead in to their investigations into e.

Purpose: This section will introduce the students to the natural base, e, by building off of their investigations in worksheet 5. This will give them an understanding of where e comes from and how the formula for continuous growth/decay is derived.

Purpose: The students will have the opportunity to model situations involving continuous growth and decay. They will apply the formulas they derived in the previous worksheet and use them to reason about the situations being modeled. They will also find and reason about the growth/decay factors in these situations.

Purpose: This section will allow students to investigate how the rate of change is related to the amount of an exponential function. The students will explore the rate of change of an investment that is growing exponentially and its relationship to the account balance at the beginning of the interval. This will build the foundation for students understanding that the rate of any exponential function is always proportional to its amount.

Purpose: This section will extend students' understanding of the proportional relationship between the amount of an exponential function and the rate that it is increasing/decreasing. They will also find the constant of propotionality and see how it is related to the situation.

Purpose: This section will introduce students to logarithms as the inverse of exponential functions. Students should come to see logarithms as exponents. They will explore how to change between logarithmic form and exponential form. There will still be an emphasis on multiplicative thinking, but now the focus will be logarithmic, or the inverse.

Purpose: This section will help deepen the students understanding of logarithms. They will use logarithms to solve problems in which the exponent is unknown. They will revisit some of the earrlier applications and be introduced to the concept of half-life.