Sections from the Glencoe Algebra I Textbook: 7.3, 7.5, 7.6, 7.7

Discovery Ed. Lessons 3.3, 8.1 & 8.2

Unit Objectives:

• Describe how the growth rate and initial value influence an exponential function.
• Graph exponential functions, interpreting the impact of the value of a, b, and c in f(x)=abx+c .
• Identify the domain and range of exponential functions.
• Calculate the average rate of change of an exponential function from a graph and a table.
• Construct exponential functions to model real-world situations.
• Describe exponential growth and decay in the context of real-world scenarios.
• Identify exponential growth and decay from equations and graphs.
• Rewrite exponential functions to interpret the function in context.
• Solve exponential equations graphically.
• Relate geometric sequences to exponential functions.
• Express exponential relationships in a variety of forms: next-now, recursive, implicit (y=ab^x), and explicit (f(x)=ab^x).
• Describe functions using multiple representations: verbally, numerically in tables, and algebraically.
• Compare linear and exponential functions.

New Jersey Student Learning Standards for this Unit:

• F-BF.A.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
• F-BF.A.1b: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
• F-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases, and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
• S-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
• F-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
• F-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
• F-IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
• F-IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
• 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).
• HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• A-REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y=f ( x ) and y=g ( x ) intersect are the solutions of the equation f ( x )=g ( x ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
• A-SSE.B.3.c: Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.15112)12t≈1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
• A-SSE.A.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
• S-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
• 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 )t10, and classify them as representing exponential growth or decay.
• F-LE.A.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
• F-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.