Lesson 3 6 Key Features of Exponential Functions

Lesson 3. 6 Key Features of Exponential Functions http: //youtu. be/FSX 1 U 8 u 7 eb 4 http: //youtu. be/Jia. STKYz 2 Vg

U. S. S. Arizona Oil-Leakage • On December 6, 1941, the USS Arizona took on a full load of fuel—nearly 1. 5 million gallons—in preparation for its scheduled trip to the mainland later that month. • The next day, much of it fed the explosion and subsequent fires that destroyed the ship following its attack by Japanese bombers. However, despite the raging fire and ravages of time, some 500, 000 gallons are still slowly seeping out of the ship’s submerged wreckage. • Nearly 70 years after its demise, the USS Arizona continues to spill up to 9 quarts of oil into the harbor each day. The oil is often referred to the “Tears of Arizona” or “Black Tears”.

U. S. S. Arizona Oil-Leakage We can take the data from the oil leakage and make a table and a graph from it. The type of graph that this data will make is what we call in math an ‘Exponential Decay’. Time (years) Annual Oil Leakage (quarts) 1941 4, 000 1990 3, 650 2006 3, 468 2009 730

Lesson 3. 6 a Key Features of Exponential Functions Concept: Characteristics of Exponential Functions Lesson EQ: How do we identify the key features of an exponential function? (Standard F. IF. 4) Vocabulary: Growth Decay Asymptote y-intercept

Exponential Functions •

Asymptote •

y-intercept •

Sketch of Graph •

Sketch of Graph •

Sketch of Graph •

Sketch of Graph •

Summary Use 20 words to teach your absent friend how to identify 2 of the following 4 features of this exponential function: f(x) = 3 x – 2 • Growth or Decay • Reflection • Asymptote • y-intercept