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Unit 5

Exponential Functions

Unit Overview 

    Exponential functions develops student ability to recognize and represent exponential growth and decay patterns, to express those patterns in symbolic forms, to solve problems that involve exponential change, and to use properties of exponents to write expressions in equivalent forms. This unit is organized into two main components. The first half of the unit explores a variety of situations involving exponential growth and the second part explores a variety of situations involving exponential decay. Each component will explore geometric sequences, exponential functions in verbal, table, graph, and equation formats, and will then explore application problems of growth and decay. In between each component, the effect of k (which represents a positive or negative constant value) is explored as it transforms the behavior of the exponential graph. Each component will consist of approximately 8-9 days. The remaining days will include pre- and post-testing of standards. Properties of exponents are reviewed in warms-ups in the beginning of the unit. Vertical and horizontal translations are reviewed in warm-ups towards the middle or the unit.


Unit Skills 

I can …
  1. identify the common ratio of the sequence.
  2. write the first and subsequent terms of the sequence.
  3. translate among recursive (NOW/NEXT), explicit, and tabular forms in modeling situations.
  4. explain the behavior of the graph when replacing f(x) by f(x) + k, and f(x + k) for specific values of k.
  5. given the graph of a function in the form f(x) = a * rx and a transformed graph, determine the value k.
  6. use appropriate technology to explore the effects of the value k on the function.
  7. construct a graph of an exponential function from a table, sequence or a situation.
  8. construct a table and/or a graph of a linear function with slope m and an exponential rate of change equal to the slope to identify the point where the exponential function exceeds the linear function.
  9. evaluate exponential functions for given domains.
  10. model an exponential relationship between two quantities with tables, graphs, and equations.
  11. classify exponential functions as growth or decay.
  12. compare/contrast properties and the graphs of linear and exponential functions.
  13. create exponential models to represent real-life data.
  14. interpret the graph and describe the pattern of change seen in the graph.
  15. find solutions to exponential equations using the graph.
  16. interpret what the parts of an expression tell you about a given situation.
  17. determine the boundaries and choose an appropriate scale when graphing an exponential function.
  18. determine the difference between the rate of change of a linear model (add each time) versus an exponential model (multiply each time)
  19. given a situation recognize which sequence (arithmetic/geometric) should be identified to interpret the model.
  20. recognize patterns to determine an arithmetic or geometric model for a sequence or problem.





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