Lesson 5: 7-5 Exponential Functions
Duration of Days: 4
Lesson Objective
Graph exponential functions.
Identify data that display exponential behavior.
How would you describe the shape of the graph of y=3^x?
In the table, how dies each whole number in the y-column compare to the previous whole number? What does this tell you about the height of consecutive points on the graph?
In the definition of an exponential function, why is it required that b ? 1?
Exponential function
Asymptote
Exponential growth function
Exponential decay function
F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
See below
Exponential functions are nonlinear and nonquadratic. An exponential function has a variable as an exponent and can be described by an equation in the form y=ab^x, where a?0, b>0, and b?1. When b>1, the function is an exponential growth function, and when 0<b<1, then the function is an exponential decay function.
Depreciation. The function V = 25000 • 0.82^t models the depreciation in the value of a new car that originally cost $25000. V represents the value of the car and t represents the time in years from the time of purchase.
Graph the function. What values of V and t are meaningful in the context of the problem?
What is the car's value after five years?
Students may interpret exponential growth or decay as a linear relationship.
Make sure students understand that the graphs of exponential functions never actually touch the x-axis.
Logical learners. Ask students to write a comparison of an exponential function to a linear function.
Practice: Exercises 1 -9
Exercises 46-50