G Exploring Exponential Models 1 x 3. y 5 2 Q 5 R Graph each function. 1. y 5 (0.3)x 6 Date 2. y 5 3x y 6 y y 4 4 2 2 x x Ϫ2 O 2 Ϫ2 O 2 x Ϫ2 O 1 4. y 5 2(3)x 5. s(t) 5 2.5t y 6 s(t) 6 f(x) 4 2 4 6 4 1 6. f (x) 5 2(5)x 2 2 2 Ϫ2 O x t x 2 1 x 7. y 5 0.99 Q 3 R decay; 0.99 Ϫ2 O Ϫ2 O 2 2 Without graphing‚ determine whether the function represents exponential growth or exponential
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EXPONENTIAL AND LOGARITHMIC FUNCTIONS I.EXPONENTIAL FUNCTION A. Definition An exponential function is a function defined by f(x) = ax ‚ where a > 0 and a ≠ 1. The domain of the function is the set of real numbers and the range is the set of positive numbers. B. Evaluating Exponential Functions 1. Given: f(x) = 2x‚ find a. f(3) = ____ b. f(5) = _____ c. f(-2) = ______ d. f(-4) = ______ 2. Evaluate f(x) = ( 1)x if 2 a. x = 2 ____ b. x = 4 _____ c. x = -3 ______ d
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Exponential and Logarithmic Functions * Verify that the natural logarithm function defined as an integral has the same properties as the natural logarithm function earlier defined as the inverse of the natural exponential function. Integrals of Exponential and Logarithmic Functions Function | Integral | lnx | x ∙ lnx - x + c | logx | (x ∙ lnx - x) / ln(10) + c | logax | x(logax - logae) + c | ex | ex+c | ek∙x | 1 / k ∙ ek∙x + c | ax | ax / lna + c | xn | 1 / (n+1) ∙ xn+1 +
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21. Optimization 2 Test 3 22. Exponential Functions 23. Logarithmic Functions 24. Compound Interest 25. Differentiation of Exponential Functions 26. Differential of Logarithmic Functions 27. Exponential Functions as Mathematical Models
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al.‚ 2012). There are two methods which are Income Smoothing and Big Bath. “Income Smoothing involves taking steps to reduce the good years and defer them for use during the business down-turn years” (Gin Chong‚ 2006). In comparison‚ Big Bath manipulation in the financial statistics indicates a great fluctuation. However‚ Income Smoothing is more ethical in accounting practice than Big Bath due to the reasons compared below. Income Smoothing has been applied in financial accounting because of
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MATH133 Unit 5: Exponential and Logarithmic Functions Individual Project Assignment: Version 2A Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. IMPORTANT: See Question 1 in Problem 2 below for special IP instructions. This is mandatory. Problem 1: Photic Zone Light entering water in a pond‚ lake‚ sea‚ or ocean will be absorbed or scattered by the particles in the water and its intensity‚ I‚ will be attenuated
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Exponential Functions in Business Turgenbayeva Aiida ID 20092726 Variant 2 Kazakhstan Institute of Management‚ Economics and Strategic Research MSC1101 Mathematics for Business and Economics Instructor: Dilyara Nartova Section #2 Summer-I 2009 Abstract This project reflects my knowledge and understanding of the interest rate‚ its types‚ formula and its evaluation in order to determine the most profitable type of investment scheme for National Bank wishing to increase
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Name:________________________________ Part 1 Exponential Functions Project There are three parts to this project. You must complete Part 1 (60 points)‚ but you may choose to do either Part 2 or Part 3 (40 points each). You may also do all three parts for a total of 140 points; however‚ you must fully complete either Part 2 or Part 3 to get credit (NOT ½ of Part 2 and ½ of Part 3). This project is due on December 5th. Turning it in late forfeits your right to extra credit and there will be
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Solving Exponential and Logarithmic Equations Exponential Equations (variable in exponent position) 1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e” nor “10”‚ use either ln or log‚ your choice.. 3. Bring the power (exponent)
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In Chapter three‚ Sanderson discusses the Boasian scholar’s criticism towards scholars work such as Tylor and Morgan on evolution and unilinear evolutionary schemes. Sanderson discussed four major objections to classical evolutionism argued by the Boasian’s this includes classical evolutionism being “logically flawed in employment of the comparative method in reconstructing evolutionary sequences”‚ classical evolutionism “employed rigid evolutionary schemes”‚ classical evolutionism “gave insufficient
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