Introduction to Exponential Functions

General Outcome:  Develop algebraic and graphical reasoning through the study of relations.

SO5. Solve problems that involve exponential equations. [C, CN, PS, R, T]

5.1 Determine the solution of an exponential equation in which the bases are powers of one another; e.g., 2^x−1 = 4^x−2 .

5.2 Determine the solution of an exponential equation in which the bases are not powers of one another; e.g., 2^x−1 = 3^x+1 .

5.3 Solve problems that involve the application of exponential equations to loans, mortgages and investments.

5.4 Solve problems that involve logarithmic scales, such as the Richter scale and the pH scale.

SO6. Represent data, using exponential and logarithmic functions, to solve problems. [C, CN, PS, T, V]

6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its graph.
6.2 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its equation.
6.3 Match equations in a given set to their corresponding graphs.
6.4 Graph data, and determine the exponential or logarithmic function that best approximates the data.
6.5 Interpret the graph of an exponential or logarithmic function that models a situation, and explain the reasoning.
6.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of exponential or logarithmic functions, and explain the reasoning.