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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