Section	Teacher-facing learning goals
Looking at Growth	Lesson 1 Compare linear and exponential relationships by performing calculations and by interpreting graphs that show two growth patterns. Lesson 2 Describe (using words and expressions) patterns in tables that represent linear and exponential relationships. Given descriptions of linear and exponential relationships, create tables of values and write expressions.
A New Kind of Relationship	Lesson 3 Explain (in writing) how to see \(a\) and \(b\) on the graph of an equation of the form \(y=a \cdot b^x\). Interpret \(a\) and \(b\) given equations of the form \(y=a \cdot b^x\) and a context of exponential growth. Write an equation of the form of \(y=a \cdot b^x\) to represent a quantity that changes by a growth factor \(b\). Lesson 4 Comprehend that the term "exponential growth" describes a quantity that changes by a growth factor that is greater than 1, and the term “exponential decay” describes a quantity that changes by a growth factor that is less than 1 but greater than 0. Use only multiplication to represent “decreasing a quantity by some fraction of itself.” Write an expression or an equation to represent a situation where a quantity decays exponentially. Lesson 5 Calculate growth factor using points on a graph that represents exponential decay. Graph equations that represent quantities that change by a growth factor between 0 and 1. Interpret equations and graphs that represent exponential decay situations. Lesson 6 Determine whether situations are characterized by exponential growth or by exponential decay given descriptions and graphs. Use graphs to compare and contrast situations that involve exponential decay. Use information from a graph to write an equation that represents exponential decay. Lesson 7 Interpret a negative exponent in equations that represent exponential growth or decay. Write and graph an equation that represents exponential decay to solve problems.
Exponential Functions	Lesson 8 Determine and explain (orally and in writing) whether relationships—in descriptions, tables, equations, or graphs—are functions. Use function notation to write equations that represent exponential relationships. Lesson 9 Determine whether a graph that represents a situation should be continuous or discrete. Interpret graphs of exponential functions and equations written in function notation to answer questions about a context. Use function notation to describe an exponential relationship represented by a graph. Use graphing technology to graph exponential functions and analyze their domains. Lesson 10 Calculate the average rate of change of a function over a specified interval. Explain (in writing) how well given rates of change reflect the changes in an exponential function. Understand that an exponential function, unlike a linear function, has different average rate of change values for different intervals. Lesson 11 Choose an appropriate model for a situation when given data. Determine graphing windows that would make a graph more informative or meaningful. Use exponential functions to model situations that involve exponential growth or decay. Lesson 12 Describe (orally and in writing) the effect of changing \(a\) and \(b\) on a graph that represents \(f(x)=a \cdot b^x\). Use equations and graphs to compare exponential functions. Lesson 13 Identify the initial value and growth factor of an exponential function given a graph showing two points with non-consecutive input values. Interpret the intersection of the graphs of two functions that represent a situation.
Percent Growth and Decay	Lesson 14 - Optional Given a starting amount and a percent increase or decrease, calculate a final amount. Write expressions using only multiplication to represent a percent increase or decrease. Lesson 15 Calculate the result of applying a percent increase repeatedly and write the result as a numerical value and expression. Use graphs to illustrate and compare situations in which different percent increases are applied to the same initial value. Write an expression of the form \((1+r)^n\) to represent a percent increase applied \(n\) times. Lesson 16 Compare the outcome of applying a percent increase, \(p\), \(n\) times to the outcome of applying the percent increase \(np\). Justify (orally and in writing) why applying a percent increase \(p\), \(n\) times, is not equivalent to applying the percent \(np\). Lesson 17 Calculate the result of repeated percent increase for the same initial balance and interest rate, but compounded at different intervals. Compare interest rates and compounding intervals to choose the better investment option. Lesson 18 Interpret and evaluate exponential expressions to solve problems. Write equivalent expressions to highlight different aspects of a situation that involves repeated percent increase or decrease.
Comparing Linear and Exponential Functions	Lesson 19 Use graphs and calculations to show that a quantity that increases exponentially will eventually surpass one that increases linearly. Use tables, calculations, and graphs to compare growth rates of linear and exponential functions. Lesson 20 Calculate rates of change of functions given graphs, equations, or tables. Use rates of change and show that, for any equal intervals of the independent variable, an exponential function always increases or decreases by an equal factor. Use rates of change to show that, for any equal intervals of the independent variable, a linear function always changes by an equal difference.
Putting It All Together	Lesson 21 Choose and write a linear or exponential function to model real-world data. Determine and explain (in writing) how well a function models the given data. Use given population data to calculate or estimate growth rates and make predictions.

Alg1.5: Introduction to Exponential Functions