# Goals for CMP3 Investigation 4

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

- Identify situations that can be modeled with 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 recognize 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
- Determine the values of the independent and dependent variables from a table, graph, or equations of an exponential function
- Use an expponential equation to describe the graph and table of an exponental 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 variety of different subejct areas, including science and business, using an equation, table, or graph
- Observe that one exponential equation can model different contexts
- Compare exponential and linear functions