Exponential Functions

13 Components
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
A2 U2: Exponential Functions
Browse Components
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 2

Exponential functions describe a common ratio at which variables change.

1 week
See Standards
Common Core: Major Standards:
N-RN.A.2

 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Common Core: Supporting Standards:
F-LE.A.2

Linear, Quadratic, & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F-IF.C.7e

Analyze functions using different representations. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-IF.C.8b

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay.

Common Core: Additional Standards:
F-LE.B.5

Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear or exponential function in terms of a context.

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

There is no Core Resource for this Big Idea.

Consider using the Instructional Routine linked below for teaching towards this Big Idea.

    Instructional Routine: Connecting Representations

    These tasks are embedded within the instructional routine called Connecting Representations.