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 5

Logarithms can be written in multiple, equivalent ways.

1 week
See Standards
Common Core: Supporting Standards:
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-LE.A.4

Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Common Core: Plus Standards:
F-BF.B.5(+)

Build new functions from existing functions.  Understand the inverse relationship between exponents and logarithms and use it to solve problems involving logarithms and exponents.

Evidence of Understanding

  • create exponential models and use them to solve problems (focus on base 2, 10, and e)
    • create a function rule from a situation, graph, or a table of values
    • recognize when to convert between exponential and logarithmic form and justify reasoning
      • Example: some problems should be converted, like 3x - 10 =19 or log4(3x) = 3, but other problems do not require conversion to be solved, like 92x - 1 = 81 or log927= x
    • convert an exponential model to a logarithm to solve for an unknown
      • evaluate the logarithm using technology
    • analyze a situation to consider viable and nonviable domain and range values
      • interpret inputs or outputs of a function in terms of the situation it models
      • compare end behavior of the exponential function with the limits of the situation
      • Example: 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
  • generate an explicit or recursive rule for a sequence and use it to solve problems
    • create a situation that could be represented by a given sequence   
    • recognize when the domain or range of a function relationship is discrete and generate a sequence that best represents corresponding outputs for a situation
      • Example: Billy measures the height of a ball, dropped from 3 meters, that rebounds to 75% of its original height after each bounce.
    • determine the sum of a finite set of terms in a situation
      • write arithmetic and geometric sequences using summation notation and use summation notation to solve problems
      • expand a series written with summation notation and use the expanded form to solve for specific inputs or outputs in a situation
      • create a situation that best models a given series written in summation notation

Develop conceptual understanding:

summation notation, sigma notation

Supporting terms to communicate:

function, input, output, domain, range, discrete, end behavior, asymptote, intercept, initial value, rate of change, growth, decay, logarithm, exponential, base, e, natural base, natural log, arithmetic, geometric

Core Resource
A core resource supports multiple days of instruction. COMING SOON!
    Instructional Routine: Contemplate then Calculate
    These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!
      Instructional Routine: Connecting Representations
      These tasks are embedded within the instructional routine called Connecting Representations. COMING SOON!