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### 9.7 Growth and Decay

Standard:

• F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions
• 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:

• How can the relationship between quantities best be represented?
• When does a function best model a situation?
• Why structure expressions in different ways?

Learning Targets:

• I know the properties of exponents. (Knowledge)
• I can apply the properties of exponents. (Application)
• I can identify the key features (intercepts, increasing/decreasing intervals, end behavior, domain/range, asymptote) of an exponential. (Knowledge)
• I can determine the domain applicable to the key features. (Application)
• I can determine if an exponential function is growth or decay when given the equation. (Application
• 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 know the parent exponential function as y = b^x. (Knowledge)
• I can classify exponential functions written in function notation as growth or decay. (Analysis)
• I can describe the rate of growth or decay in context. (Comprehension)
• I can determine the growth or decay factor of an exponential function. (Application)
• 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)
Warm-Up:
Notes:

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Video:

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