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Do Now Rhonda hears a rumor at 8:00 A.M. She immediately tells her two best friends the rumor. One hour later Rhonda’s friends have each told two of their friends. This pattern continues each hour, with each friend reporting the rumor to two friends who have not already heard it. By 8:00 P.M. that evening, how many people have heard the rumor? Answer: 8191 Chapter 8 Section 1 Exponential Growth Mr. Ochoa Algebra II Vocabulary • • • • Exponential FunctionBaseAsymptoteExponential Growth Function• Growth Factor- Objective - To graph exponential functions and to model them in real-life situations. Examples y 12(5) x y 0.2(3.8) Exponential Growth Function An equation of the form y a b . With a 0, b 0. x x Graph y 3 x y 2 1 / 9 1 1 / 3 0 1 1 3 2 9 3 27 4 81 5 243 x y x Graph y 3 x y y-intercept = 1 asymptote = x-axis domain: all real numbers range: y > 0 x 1 x Graph y 2 4 x y 2 0.0625 1 0.125 0 0.25 1 0.5 2 1 3 2 4 4 5 8 6 16 y x 1 x Graph y 2 4 y y-intercept = 0.25 asymptote = x-axis domain: all real numbers range: y > 0 x Graph y 2 3 1 x y x y 2 0.8 1 0.3 0 1 1 5 2 17 3 53 x Graph y 2 3 1 x y y-intercept = 1 asymptote y = -1 domain: all real numbers range: y > -1 x Exponential Growth y a(1 r)t a initial amount r % increase 1 r is the growth factor t number of time periods In 2005 the average price of a car was $15,000. If the price increases 8% a year, what will the average price be in 10 years? y 15,000(1 .08) 10 y $32, 384 Compound Interest r A P 1 n nt P initial principal deposited r annual rate n = compounded times per year t years You deposit $50,000 in an investment account that pays 6% annual interest. Find the balance after 2 years if the interest is compounded quarterly ? r A P 1 n nt P = 50,000, r = 0.06 n = 4, t = 2 0.06 A 50, 000 1 4 A $56, 324.63 4 2