HW01.pdf - young(toy68 HW01 villafuerte altu(53780 This...

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young (toy68) – HW01 – villafuerte altu – (53780) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Find the smaller solution of the exponential equation 3 x 2 = 9 - 1 2 x +6 . 1. none of these 2. x = - 3 3. x = 3 4. x = - 4 correct 5. x = 4 Explanation: By properties of exponents, 9 - 1 2 x +6 = 3 - x +12 . Thus the equation can be rewritten as 3 x 2 = 3 - x +12 , which after equating exponents becomes x 2 = - x + 12 . This equation factors as ( x - 3)( x + 4) = 0 , and so its solutions are x = 3 , - 4. Hence the smaller solution is x = - 4 . 002 10.0points If a, b are the solutions of the exponential equation 4 x 2 = 16 5 2 x - 3 , calculate the value of ab . 1. ab = - 5 2. ab = - 6 3. ab = 4 4. ab = 8 5. ab = 6 correct Explanation: By properties of exponents, 16 5 2 x - 3 = 4 5 x - 6 . Thus the equation can be rewritten as 4 x 2 = 4 5 x - 6 , which after taking logs to the base 4 becomes x 2 = 5 x - 6 . This equation factors as ( x - 3)( x - 2) = 0 , and so its solutions are 3 , 2. Hence ab = 6. 003 10.0points If x 1 , x 2 are the solutions of the equation 8 4 x 2 = 1 64 4 x +1 , compute the value of | x 1 - x 2 | . 1. | x 1 - x 2 | = - 8 2 2. | x 1 - x 2 | = - 2
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young (toy68) – HW01 – villafuerte altu – (53780) 2 3. | x 1 - x 2 | = 8 2 correct 4. | x 1 - x 2 | = 8 4 5. | x 1 - x 2 | = 2 Explanation: Since 1 64 4 x +1 = 8 - 8 x - 2 , the equation can be written as 8 4 x 2 = 8 - 8 x - 2 , which in turn can be rewritten as 4 x 2 = - 8 x - 2 by taking logs to the base 8 of both sides. By the quadratic formula, therefore, x 1 , x 2 = - 4 ± 8 4 . Thus | x 1 - x 2 | = 8 2 . 004 10.0points Find y when 2 x = 16 y , 16 x = 32 y +2 . 1. y = 1 2. y = 8 11 3. y = 9 11 4. y = 12 11 5. y = 10 11 correct Explanation: The equations 2 x = 16 y , 16 x = 32 y +2 are equivalent to 2 x = 2 4 y , 2 4 x = 2 5( y +2) . Now set v = 2 x and u = 2 y . Then v = u 4 , v 4 = 1024 u 5 . Substituting for v in the second equation we thus get u 16 = 1024 u 5 , i . e ., u = 2 10 11 . Consequently, since u = 2 y , y = 10 11 . 005 10.0points Which function has 2 4 - 2 - 4 2 4 - 2 - 4 as its graph? 1. f ( x ) = 2 - 2 - x - 1 2. f ( x ) = 2 - x - 1 - 2 3. f ( x ) = 3 x - 3 4. f ( x ) = 2 x - 1 - 3 correct 5. f ( x ) = 2 - 3 - x
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young (toy68) – HW01 – villafuerte altu – (53780) 3 6. f ( x ) = 3 - x - 2 Explanation: The given graph has the property that lim x → -∞ f ( x ) = - 3 . But lim x → ∞ 2 - x = 0 = lim x → ∞ 3 - x , while lim x → -∞ 2 x = 0 = lim x → -∞ 3 x , so f ( x ) must be one of 2 x - 1 - 3 , 3 x - 3 . On the other hand, the y -intercept of the given graph is at y = - 5 2 . Consequently, the graph is that of f ( x ) = 2 x - 1 - 3 . 006 10.0points Which exponential function f ( x ) = c x + b + a has 2 4 6 8 - 2 - 4 - 6 - 8 2 4 6 - 2 - 4 - 6 - 8 - 10 for its graph and the line y = - 7 for horizontal asymptote.
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  • Fall '09
  • GOGOLEV
  • Exponentiation, Inverse function, Natural logarithm, Logarithm, villafuerte altu

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