1. Chapter 1.3 Exponential Functions

2. Exponential function F(x) = a x The domain of f(x) = a x is (-∞, ∞) The range of f(x) = a x is (0, ∞)

3. Graphing an Exponential Function Graph the function y = 2(3 x ) – 4 State the domain and range Domain is (-∞, ∞) Range is (-4, ∞)

4. Rules for Exponents If a > 0 and b > 0, the following hold for all real numbers x and y. 1) a x  a y = a x+y 2) a x /a y = a x-y 3) (a x ) y = a xy 4) a x  b x = (ab) x 5) (a/b) x = a x /b x 6) a -1 = 1/a

5. Exponential Regression Use the following table to predict the US population in the year 2020 Find an exponential equation to fit the data Find the population in 2070 yearpopulation 2005276.1 2006279.3 2007282.4 2008285.3 2009288.2 2010291.0

6. Exponential growth vs Exponential Decay A substance decrease is mass over time such as radioactive decay The function y = k  a x is exponential growth is a > 1 The function y = k  a x is exponential decay is 1 > a > 0

7. The Number e Known as the natural number e = 2.718281828 Banks use compounded continuously y = P  e rt P = initial investment, r = rate, t = time(years), y = investment after t years Find y where p = $10,000, r = 5%, t = 25 years

8. Homework Pg 26 #1-5 Quick Review Pg 26 # 1-21 odd