APPLICATIONS OF EXPONENTIAL| AND| LOGARITHMIC FUNCTIONS| EARTHQUAKE WORD PROBLEMS: As with any word problem‚ the trick is convert a narrative statement or question to a mathematical statement. Before we start‚ let’s talk about earthquakes and how we measure their intensity. In 1935 Charles Richter defined the magnitude of an earthquake to be where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the
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Exponential and Logarithmic Functions 2.2 Logarithmic Functions MATH14 • Logarithmic Function with base b • Graph of Logarithmic Function • Natural Logarithmic Function • Properties of Logarithmic Functions • Exponential and Logarithmic Equations Logarithmic Function with base b Definition: The logarithmic function with base b is the inverse of the exponential function with base b. y logb x Note: Dom f if and only if x b y Rng f Logarithmic Function
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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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Exponential Smoothing Forecasting Method with Naïve start Formula: Ft = α (At-1) + (1 – α) (Ft – 1) where: Ft Forecast for time t Ft – 1 Past forecast; 1 time ahead or earlier than time t At-1 Past Actual data; 1 time ahead or earlier than time t α (read as alpha) as a smoothing constant takes the
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Exponential Functions An exponential function is in which a constant base is raised to a variable power. Exponential functions are used to model changes in population size‚ in the spread of diseases‚ and the growth of investments. They can also accurately predict types of decline typified by radioactive decay. The essence of exponential growth‚ and a characteristic of all exponential growth functions‚ is that they double in size over regular intervals. The most important exponential function is
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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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following- high speed‚ low power consumption‚ less area‚ more accuracy or even combination of them in multiplier. However‚ in multiplier design for reducing time and power consumption there are many practical solutions‚ like truncated and logarithmic multipliers. These methods consume less time and power but introduce errors. Nevertheless‚ they can be used in situations where a shorter time delay is more important than accuracy. But‚ in many applications where accuracy is prime criteria they
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fePolar coordinates are two-dimensional and thus they can be used only where point positions lie on a single two-dimensional plane. They are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point. For instance‚ the examples above show how elementary polar equations suffice to define curves—such as the Archimedean spiral—whose equation in the Cartesian coordinate system would be much more intricate. Moreover‚ many physical
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relationships with the aristocracy‚ the towns‚ and the church. The worldwide trend of urbanization has changed over time as well as changing the functions of cities. The cities represent a world of opportunity which links with urbanization and economic growth. The cities are also home to a high concentration of povertys. The urban areas have
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