Exponential Functions Algebra 1/Ms. Wiggins 2-20-18 Part 1

Objective SWBAT: Sketch graphs showing key features of exponential functions. Write exponential functions using tables and graphs.

Vocabulary Asymptote Constant Ratio Exponential Function

Essential Understanding An Exponential function models the relationship between two quantities that differ by a constant ratio. Exponential functions are modeled using f(x)= 𝑎𝑏 𝑥 where a is the initial amount and b is the constant ratio.

Asymptote A line that the function gets closer and closer to, but never touches it.

Example 1 Page 224 There are key features and characteristics of the graphs of exponential functions that help distinguish them from other functions. What patterns do you notice in the table? What key features can be identified from the graph of an exponential function? What is an asymptote and why do exponential functions have one? Students Do: Try it page 225

Exponential Growth and Decay Algebra 1 2-26-18 Ms. Wiggins

Objective Construct exponential growth and decay functions given a description of a relationship. Recognize if a situation can be modeled with exponential growth or decay, and interpret the parameters of the modeled context.

Essential Understanding An exponential growth function increases by a fixed percent over each interval. An exponential decay function decreases by a fixed percent over each interval. Exponential growth and decay functions can be used to model many real-world situations.

Vocabulary Compound interest Decay factor Exponential growth Exponential decay Growth factor

𝑓(𝑥) = 𝑎𝑏 𝑥 𝑦= 𝑎𝑏 𝑥 𝑦= 𝑎𝑏 𝑥 0<𝑏<1 Exponential Decay 𝑦= 0.5 𝑥 𝑓(𝑥) = 𝑎𝑏 𝑥 𝑦= 𝑎𝑏 𝑥 𝑦= 𝑎𝑏 𝑥 0<𝑏<1 Exponential Decay 𝑦= 0.5 𝑥 0.5 = Decay Factor 𝑏>1 Exponential Growth 𝑦=2 𝑥 2 = Growth Factor

Pearsonrealize.com examples 1 & 2