1. Algebra II w/ trig

2. Exponential Functions – has the form y= ab x, where a ≠0, b>0, and b≠1 - y represents the quantity after time is expired - a represents the initial quantity and the y intercept - b represents the base - x represents the time

3. I. 2 types of exponential functions Exponential Growth: if a>o and b>1 Exponential Decay: if a>o and 0< b <1 A. Exponential Growth or Decay? 1. y = 0.3(1.2) x 3. y = 3(0.6) x 2. y = -5 ( 4 / 5 ) x 4. y = 5(4) -x

4. B. Sketch the graph and state the domain and the range. Parent equation: y = ab x With shifts y = ab x-h + k To graph:1. Sketch y= ab x, use a table with x values 0 and 1 2. Then move your 2 points h units left or right, and k units up or down 3. Then sketch the graph with the 2 new points

5. a. f(x) = (½) x b. f(x) = 3 x

6. c. f(x)= 3 ●2 x-1 – 4d. f(x) = 2 ●3 x-2 + 1

7. II. Exponential Equations/ Inequalities A. Properties of Rational Exponents a. a m ●a n = a m+n b. (a m ) n = a mn c. a m ÷ a n = a m-n B. Simplify each expression. a. (3 √2 ) √2 e. (x √6 )(x √5 ) b. (m √28 ) √7 f. 2x π (5x 3π ) c. (c √6 ) √63 g. 25 √2 ● 125 √2 d. (x √6 y 3√2 ) √2

8. C. Property of Equality for Exponential Functions If b is a positive number other than 1, then b x = b y, if and only if x = y D. Property of inequality of Exponential Functions If b > 1, then b x > b y, if and only if x > y, and b x < b y, if and only if x< y

9. E. Solve each equation or inequality. Check your solutions. a. 2 x+1 = 2 2x + 3 b. 3 2x-1 = 3 x+2

10. c. 4 x+1 = 8 2x+3 d. 2 3x = 4 x+2 e. 3 2x-1 = 1 / 9 f. g x-2 = 1 / 16

11. g. 4 √x = 16 √5 h. 3 x-4 < 1 / 27 i. 4 2x-2 >2 x+1 j. 5 2x <125 x-5