Big Idea:

Big Idea 2

Exponential functions describe a common ratio at which variables change.

1 week

Evidence of Understanding

  • use rate of change to define exponential functions (focus on base 2, 10, and e)
    • identify an asymptote and justify its existence
    • explain why an exponential function does not have turning points (mins or maxs)
    • distinguish exponential growth from decay from a graph, table, sequence, or situation
      • identify quantities and words that indicate exponential growth or decay
    • analyze situations, graphs, and tables to justify an exponential function model (versus other models)
      • introduce the natural base (base e) to model situations that continuously change
    • given 3+ data points, calculate the base (growth or decay rate) of the exponential function
  • create representations of exponential functions(focus on base 2, 10, and e)
    • identify the initial value and common ratio of change from a situation, sequence, table or graph
    • generate an exponential graph, table, explicit function rule, or recursive function rule
    • connect features of exponential functions across representations
      • match an exponential function rule with a sequence, situation, table or graph
      • Ex: recognize “an 8% annual increase” models exponential growth with a base of 1.08
  • evaluate exponential functions(focus on base 2, 10, and e)
    • calculate exact output values given an input
    • evaluate an expression or equation written in function notation from a graph, table, or equation
      • Ex: evaluate f(3) by looking at the points on graph or in the table
    • analyze a situation to consider viable and nonviable domain and range values
      • compare end behavior of the exponential function with the limits of the situation
      • Ex: continuous exponential functions have no limits on the domain but in a situation there may be limits to how much the outputs can grow or decay

Develop conceptual understanding:

asymptote, exponential growth, exponential decay, natural base e, base


Supporting terms to communicate:

function, independent, dependent, input, output, domain, range, ratio, initial value, function rule, function notation, end behavior, intercept, rate of change
Core Resource
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    Instructional Routine: Contemplate then Calculate
    These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!