mac1105_lecture22_1

mac1105_lecture22_1 - L22 Exponential Functions Statement:...

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239 L22 Exponential Functions Statement : If a and x are real numbers with 0 a > and 1 a , then x ya = is a uniquely defined real number. Laws of Exponents If s , t , a , and b are real numbers, with 0 a > , 0 b > , then st s t aa a + ⋅= s t a a a = () s t = 0 1 a = ss s ab a b =⋅ s s s bb ⎛⎞ = ⎜⎟ ⎝⎠ 11 s s s a == The exponential function with the base a is a function of the form x fx a = , where 0 a > and 1 a . The domain of f is the set of all real numbers.
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240 Example : For ( ) x fx c a = , ( 0 a > , 1 a , 0 c ) evaluate (1 ) () fx + = Example : For ( ) fx a x b = + ( 0 a ), evaluate ) ( ) +− = Comparing Exponential and Linear Models : For an exponential model , x a = ( 0 a > , 1 a , 0 c ), for unit increases in the input, the output changes by a factor of a (base) ) ( ) + =⋅ . For a linear model , ( ) = + ( 0 a ), for unit increases in the input, the output changes by an additive a (slope) ) ( ) + =+ .
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241 Example : Find the appropriate model for each of the problem. (a) Wages of an Assembly Line Worker : A manufacturer pays its assembly line workers $11.50 per hour. In addition, workers receive a piecework rate of $0.75 per unit produced. Write the equation for the hourly wages W in terms of the number of units x produced per hour.
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This note was uploaded on 11/07/2011 for the course MAC 1105 taught by Professor Picklesimer during the Fall '10 term at University of Florida.

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mac1105_lecture22_1 - L22 Exponential Functions Statement:...

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