# Goals for CMP3 Problem 5.1 Looking for Patterns Among Exponents

**Exponential Functions** Explore problem situations in which two or more variables have an exponential relationship to each other

- Identify situations that can be modeled by an exponential function
- Identify the pattern of change (growth/decay factor) between two variables that represent an exponential function in a situation, table, graph or equation
- Represent an exponential function with a table, graph or equation
- Make connections among the patterns of change in a table, graph, and equation of an exponential function
- Compare the growth/decay rate and growth/decay factor for an exponential function and recognizie the role each plays in an exponential situation
- Identify the growth/decay factor and initial value in problem situations, tables, graphs and equations that represent exponential functions
- Determine whether an exponential function represents a growth (increasing) or decay (decreasing) pattern, from an equation, table or graph that represents an exponential function
- Use an exponential equation to describe the graph and table of an exponential function
- Predict the
*y*-intercept from an equation, graph or table that represents an exponential function - Interpret the information that the
*y*-intercept of an exponential function represents - Determine the effects of the growth factor and initial value for an exponential function on a graph of the function
- Solve problems about exponential growth and decay from a vairety of different subject areas, including sciences and business, using an equation, table or graph
- Observe that one exponential equation can model different contexts
- Compare exponential and linear functions

**Equivalence** Develop understanding of equivalent exponential expressions

- Write and interpret exponential expressions that represent the depends variable in an exponential function
- Develop the rules for operating with rational exponents and explain why they work
- Write, interpret, and operate with numerical expressions in scientific notation
- Write equivalent expressions using the rules for exponents and operations
- Solve problems that involve exponents, including scientific notation