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Unformatted text preview: Rules for exponents a x a y = a x + y a x a y = a x y if a 6 = 0 ( a x ) y = a xy a x b x = ( ab ) x a x b x = ( a b ) x if b 6 = 0 a 1 /n = n a a = 1 if a 6 = 0 a x = 1 a x if a 6 = 0 WARNING: 0 is not defined and 0 x for x > 0 has no value. Problem Set 1. A beaker containing bacteria is left to sit in the lab. This bacteria divides once every minute, doubling the volume in the beaker. If the beaker was left out for 60 minutes, when was the beaker 1 / 4 full? (58 minutes) 2. Solve 2 30 = n 10 . ( n = 8) 3. Solve 2 2 = 8 k . ( k = 1 2 ) 4. Solve 2 3 4 n +5 = 8 2 n 1 . ( n = 5 4 ) 5. Simplify: 6 a 2 b 2 a 3 b 3 a 2 (2 a b 3 2 b 3 a ) 6. Sherri plans to retire in 5 years. She has $10,000 in a savings account with a 50% interest rate. If the interest compounds yearly, how much will she have? What about if it compounds monthly, weekly, daily, (or continuously)? (Assuming 1 year, 12 months, 52 weeks, 365 days gives $75937 . 50 , $115804 . 66 , $120378 . 67 , $121616 . 70, $121824.94) 7. If m and k are integers, find all solutions to the equation 9(7 k + 7 k +2 ) = 5 m +3 + 5 m . ( m = 2, k = 1) 8. If 2 x +3 + 2 x = 3 y +2 3 y and x and y are integers, determine the values of x and y . ( x = 3,...
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 Fall '10
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 Linear Algebra, Algebra, Exponents

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