Chapter 9‎ > ‎

### 9.6 Exponential Functions

Standard:

• F.IF.C.7.E: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
• F.IF.C.8.B: 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.
• F.LE.A.1.C: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
• F.LE.A.1.A: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
• F.LE.A.2: 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.LE.A.3: Observe using graph and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
• F.LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
• A.SSE.B.3.C: Use the properties of exponents to transform expressions for exponential functions

Essential Questions:

• When does a function best model a situation?
• Why structure expressions in different ways?

Learning Targets:

• I can graph exponential functions.  (Synthesis)
• I can identify the key features (intercepts, increasing/decreasing intervals, end behavior, domain/range, asymptote) of an exponential. (Knowledge)
• I know the parent exponential function as y = b^x.  (Knowledge)
• I can determine the domain applicable to the key features.  (Application)
• I can classify exponential functions written in function notation as growth or decay.  (Analysis)
• I can generate a table of values in order to graph exponential functions.  (Synthesis)
• I can interpret the initial value of an exponential function in the context of a problem.  (Evaluation)
• I can identify situations that can be modeled by exponential situations.  (Knowledge)
• I can describe the rate of growth or decay in context.  (Comprehension)
• I can distinguish between linear and exponential models.  (Comprehension)
• I can determine the growth or decay factor of an exponential function.  (Application)
• I can determine if a function is linear or exponential based on a sequence.  (Application)
• I can determine if a function is linear or exponential based on a table.  (Application)
• I can determine if a function is linear or exponential based on a graph.  (Application)
• I can determine if a function is linear or exponential based on a verbal description.  (Application)
• I can create a system of equations given two points to find the values needed to write an exponential equation.   (Synthesis)
• I can compare output values of any functions using graphs or tables.  (Analysis)
• I can estimate when intervals of one function is greater than another function.  (Evaluation)
• I can compare rates of change of functions using graphs or tables.  (Evaluation)
• I can explain why exponential functions eventually have greater output values than other functions.  (Evaluation)
• I can identify the parts of an exponential function and their impact on the graph.  (Knowledge)
• I can explain the meaning using appropriate units of the constant a of an exponential function given real world situation.  (Evaluation)
• I can explain the meaning using appropriate units of the constant b of an exponential function given real world situation.  (Evaluation)
• I can explain the meaning using appropriate units of the constant c of an exponential function given real world situation.  (Evaluation)
• I can explain the meaning using appropriate units of the y-intercept and other points  of an exponential function given real world situation.  (Evaluation)
• I can compose an original problem and model it with an exponential function.  (Synthesis)
• I can define an exponential function.  (Knowledge)

Warm-Up:

Notes:

Click on the image below for the PDF of the notes 9.6 Exponential Functions

Video:

Click below for the Classroom Lesson -  9.6 Exponential Functions

Watch this video on Exponential Functions

Watch this video on Exponential Functions

Activities:

Click on the image below for a review -  Exponential Functions

Click on the image below for a review -  Exponential Functions

Assessment/Homework:
pg. 570 11-19 odd