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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Cartesian Coordinate System 4. Straight Lines 5. Functions and their Graphs 6. The Algebra of Functions 7. Functions and Math Models 8. Limits Test 1 9. The Derivative 10. Basic Rules of Differentiation 11. The Product and Quotient Rules 12. The Chain Rule 13. Marginal Functions in Economics 14. Higher-Order Derivatives 15. Implicit
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sum as i runs from 1 to n of the ai 4. Linear algebra ‖x‖the norm (or modulus) of x OA→OA / vector OA OA¯ OA / the length of the segment OA AT A transpose / the transpose of A A−1 A inverse / the inverse of A 5. Functions f(x) fx / f of x / the function f of x f:S→T a function f from S to T x→y x maps to y / x is sent (or mapped) to y f’(x) f prime x / f dash x / the (first) derivative of f with respect to x f”(x) f double-prime x / f double-dash x / the second derivative of f
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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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and uses of several kinds of algebraic functions. The four models include‚ linear‚ exponential‚ power‚ and inverse power. The purpose of this assignment is to review our understanding of these models and their uses and to fulfill a writing piece for the MEAP test. The first and simplest function to be discussed is the linear function. A linear function can be modeled by the equation f(x)=ax+b‚ where a is the slope and b is the y-intercept. Linear functions form a straight line when graphed and maintain
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Choose one of the forecasting methods and explain the rationale behind using it in real life. I would choose to use the exponential smoothing forecast method. Exponential smoothing method is an average method that reacts more strongly to recent changes in demand than to more distant past data. Using this data will show how the forecast will react more strongly to immediate changes in the data. This is good to examine when dealing with seasonal patterns and trends that may be taking place. I would
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Demand Forecasting Problems Simple Regression a) RCB manufacturers black & white television sets for overseas markets. Annual exports in thousands of units are tabulated below for the past 6 years. Given the long term decline in exports‚ forecast the expected number of units to be exported next year. |Year |Exports |Year |Exports | |1 |33 |4 |26
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