2.4.1 MATHPOWER TM 12, WESTERN EDITION 2.4 Chapter 2 Exponents and Logarithms

To solve exponential equations, you need to apply the Laws of Exponents. One method of solving exponential equations is based on the following property: If a x = a y, then x = y. That is, if 2 powers are equal and have the same bases, then the exponents are equal. Solve the following: a) 9 2x - 3 = 27 x + 4 (3 2 ) 2x - 3 = (3 3 ) x x - 6 = 3 3x + 12 Since both sides have the same base, then the exponents must be equal: 4x - 6 = 3x + 12 x = 18 b) 16 2x + 4 = x + 4 = x + 4 = 0 2x = -4 x = Solving Exponential Equations

(3 2 ) x + 2 = (3 -3 ) x x + 4 = 3 -3x - 6 2x + 4 = -3x - 6 5x = - 10 x = -2 x 2 = 5x - 4 x 2 - 5x + 4 = 0 (x - 4)(x - 1) = 0 x - 4 = 0 or x - 1 = 0 x = 4 or x = Solving Exponential Equations -3x + 6 = 4x x = 7 x = -1

Exponential Growth A cell doubles every 4 min. If there are 500 cells originally, how long would it take to reach cells? N(t)N(t)Number of bacteria after t minutes NoNo Number of bacteria originally tTime passed dDoubling time t = 20 Therefore, it would take 20 min for the cells to reach

Exponential Decay The half-life of sodium 24 is 15 h. How long would it take for 1600 mg to decay to 100 mg? A(t)A(t)Amount after a given period of time AoAo Amount originally tTime passed hHalf-life t = 60 It would take 60 h to decay to 100 mg

Suggested Questions: Pages 89 and , 24, 30, 32, 34 a Page 93 all 2.4.6