Section	Teacher-facing learning goals
Growing and Shrinking	Lesson 1 Compare and contrast (orally) exponential growth and decay. Determine values of simple exponential functions in context. Lesson 2 - Optional Explain (in writing) the meaning of different constants in an expression representing an exponential function. Interpret equations and graphs that represent exponential functions in context.
Understanding Non-Integer Inputs	Lesson 3 Understand the meaning of a rational input, particularly positive non-whole number inputs, to an exponential function in context. Use equations and graphs to identify the value of an exponential function at a rational input. Lesson 4 Interpret fractional inputs for exponential functions in context. Understand that the growth (or decay) factor for an input interval of \(\frac{1}{n}\) is \(b^{\frac{1}{n}}\) and not \(\frac{b}{n}\) when \(b\) is the growth (or decay) factor for an interval of length 1 and \(n\) is the number of intervals. Lesson 5 Understand that an exponential function still changes by a constant factor over equal intervals, even if the interval is a fractional amount. Lesson 6 Create an equation for an exponential function from input-output pairs in which the inputs do not differ by 1. Determine what information is needed to write an exponential equation. Ask questions to elicit that information. Lesson 7 Comprehend the term “half-life” in relation to the radioactive decay of certain elements and use it to calculate the age of different objects. Describe (in writing) the parameters of exponential expressions that represent different decay situations.
Missing Exponents	Lesson 8 Comprehend the need to "undo" exponentiation to solve problems in simple contexts. Explain (orally and in writing) how to determine the value of an unknown exponent both exactly and approximately. Lesson 9 Comprehend the definition of a logarithm as the solution to an exponential equation. Identify the parameters in expressions involving a logarithm. Lesson 10 Coordinate (orally and in writing) exponential and logarithmic equations that represent the same relationship. Create equivalent equations in exponential and logarithmic forms. Lesson 11 Calculate the value of a logarithmic expression using estimation or technology. Justify (orally) why one logarithmic expression is greater than another.
The Constant e	Lesson 12 Comprehend that \(e\) represents a constant whose value is approximately 2.718. Lesson 13 Comprehend that we can use \(e^r\) as the growth factor of \(f(t) = e^{rt}\) when we assume the rate \(r\) is applied continuously. Interpret the parameters in the equations of exponential functions with the form \(f(t)=P \cdot e^{rt}\). Lesson 14 Comprehend that the natural logarithm is used to express the solution to an exponential equation with base \(e\). Use base 10 and natural logarithms to solve exponential equations.
Logarithmic Functions and Graphs	Lesson 15 Use graphs to identify solutions to exponential equations. Use logarithms to calculate solutions to exponential equations. Lesson 16 Calculate the coordinates of the point of intersection of two exponential graphs using logarithms. Interpret the intersection of the graphs of two exponential functions in context. Lesson 17 Create graphs of logarithmic functions and use them to answer questions. Describe (orally and in writing) characteristics of logarithmic functions. Lesson 18 - Optional Use logarithmic relationships to solve problems about acidity and earthquakes.

Alg2.4: Exponential Equations and Functions