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3.1 Exponential Functions.notebook Warmup work in pairs March 19, 2018 3/19/18 Sketch and analyze the graph of each. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing. 1. f (x) = 4x 2. f (x) = 5–x a. Domain: b. Range: c. Xint: d. Yint: e. Asymptote: f. End Behavior: g. Increasing: h. Decreasing: a. Domain: b. Range: c. Xint: d. Yint: e. Asymptote: f. End Behavior: g. Increasing: h. Decreasing: non-calc 3.1 2 parts Exponential Functions 3.1 Exponential Functions.notebook March 19, 2018 f(x) = 2x Example 1 The Natural Base e e = 2.71821828… is called the natural base. It is used in many applications and is important in calculus. Natural Exponential Graph Graph and find the following: f(x) = 2x − 3 + 5. a. Parent Function: b. Domain: c. Range: d. Xint: e. Yint: f. Asymptote: g. End Behavior: 3.1 Exponential Functions.notebook March 19, 2018 Example 2 Graph and find the following: f(x) = 2(3)4 x 6. a. Parent Function: b. Domain: c. Range: d. Xint: e. Yint: f. Asymptote: g. End Behavior: Example 3 Graph and find the following: f(x) = ex − 3 2. a. Parent Function: b. Domain: c. Range: d. Xint: e. Yint: f. Asymptote: g. End Behavior: Example 4 Mrs. Salisman invested $2000 into an educational account for her daughter when she was an infant. The account has a 5% interest rate. If Mrs. Salisman does not make any other deposits or withdrawals, what will the account balance be after 18 years if the interest is compounded: a. quarterly? b. monthly? c. daily? d. continuously? 3.1 Exponential Functions.notebook March 19, 2018 Example 5 In addition to investments, populations of people, animals, bacteria, and amounts of radioactive material can also change at an exponential rate. Exponential growth and decay models apply to any situation where growth is proportional to the initial size of the quantity being considered. A state’s population is declining at a rate of 2.6% annually. The state currently has a population of approximately 11 million people. If the population continues to decline at this rate, predict the population of the state in 15 and 30 years. HW • 3.1 Worksheet • Textbook: pg 166-168 #24-36 (mult. of 4) 38-56 even, 60-64 even