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# Topic: Exponential function

 Exponential function - Wikipedia, the free encyclopedia The exponential function is one of the most important functions in mathematics. The importance of exponential functions in mathematics and the sciences stems mainly from properties of their derivatives. The exponential function maps any line in the complex plane to a logarithmic spiral in the complex plane with the center at the origin. en.wikipedia.org /wiki/Exponential_function   (1112 words)

 Exponential function   (Site not responding. Last check: 2007-10-22) The exponential function on the complex plane is a holomorphic function which is periodic with imaginary period 2πi which can be written as This formula connects the exponential function with the trigonometric functions, and this is the reason that extendingthe natural logarithm to complex arguments yields a multi-valued function ln(z). It is easy to see, that the exponential function maps any line in the complex plane to a logarithmic spiral in the complex plane with the centre at 0,noting that the case of a line parallel with the real or imaginary axis maps to a line or circle. www.therfcc.org /exponential-function-23760.html   (642 words)

 Characterizations of the exponential function - Wikipedia, the free encyclopedia In mathematics, the exponential function can be characterized in many ways. For instance, when the value of the function is defined by a sequence or series, the convergence of this sequence or series needs to be established. In this case, we define the natural logarithm function ln(x) first, and then define exp(x) as the inverse of the natural logarithm. en.wikipedia.org /wiki/Characterizations_of_the_exponential_function   (673 words)

 PlanetMath: complex exponential function The complex exponential function is usually denoted in power form: The function gets all complex values except 0 and is periodic having the prime period (the period with least non-zero modulus) This is version 13 of complex exponential function, born on 2004-10-10, modified 2006-07-22. planetmath.org /encyclopedia/ExponentialFunction2.html   (191 words)

 Exponential Functions   (Site not responding. Last check: 2007-10-22) When exponential growth and decay are described with exponential functions the variable "t" is used to represent time. As stated before, the exponential function can be used to determine the growth and decay of populations or substances. By examining data the exponential function was found to be a good model for the data. dwb.unl.edu /Teacher/NSF/C03/C03Mats/ExpFns.html   (1018 words)

 PlanetMath: exponential function It is infinitely differentiable, and the derivative is the exponential function itself Since the exponential function obeys the rules normally associated with powers, it is often denoted by This is version 12 of exponential function, born on 2002-02-23, modified 2005-06-08. www.planetmath.org /encyclopedia/ExponentialFunction.html   (332 words)

 Exponential and Logarithmic Equations Some exponential equations can be solved by using the fact that exponential functions are one-to-one. When solving exponential equations we frequently used logarithmic identity 1 because it involves applying a logarithmic function to "undo" the effect of an exponential function. Since log is the logarithm base 10, we apply the exponential function base 10 to both sides of the equation. www.uncwil.edu /courses/mat111hb/EandL/equations/equations.html   (539 words)

 1.3.6.6.7. Exponential Distribution The formula for the inverse survival function of the exponential distribution is Maximum likelihood estimation for the exponential distribution is discussed in the chapter on reliability (Chapter 8). The exponential distribution is used to model data with a constant failure rate (indicated by the hazard plot which is simply equal to a constant). www.itl.nist.gov /div898/handbook/eda/section3/eda3667.htm   (318 words)

 MTH 207 Lab Lesson 11 - Exponential Functions Thus the ratio of a exponential functions at equal distance are equal. The exponential function has the property that it is its own derivative, i.e. In particular the natural logarithm ln(x) is the inverse of the exponential function. www.scs.ryerson.ca /~danziger/labs/less11.htm   (462 words)

 Exponential Functions Exponential functions are functions of the form f(x) = b Exponential functions are characterized by the fact that their rate of growth is proportional to their value. Populations might exhibit exponential growth in the absence of constraints, while quantities of a radioactive isotope exhibit exponential decay. oregonstate.edu /instruct/mth251/cq/FieldGuide/exponential/lesson.html   (310 words)

 exponential function The variable x in the equation is called the 'exponent', the function is called the exponential function. as base of the power, the function is the natural exponential function exp(x), sometimes abbreviated as exponential function. A force for which the potential is an exponential function of the distance (with negative exponent). www.2dcurves.com /exponential/exponentiale.html   (869 words)

 Exponential function It is written as exp(x) or $e^x$ (where e is the base of the natural logarithm) and can be defined in two equivalent ways, the first an infinite series, the second a limit: The major importance of the exponential functions in the sciences stems from the fact that they are constant multiples of their own derivatives: The exponential function on the complex plane is a holomorphic function which is periodic with imaginary period $2 \pi i$ which can be written as www.ebroadcast.com.au /lookup/encyclopedia/ex/Exp.html   (728 words)

 exponential function properties   (Site not responding. Last check: 2007-10-22) exponential function exponential function We begin by defining the exponential function... Exponential Function -- from MathWorld Exponential Function -- from MathWorld The exponential function is the entire function defined by \mathop{\rm exp}\nolimits (z) \equiv e^z, where e is the constant 2.718.... Objectives: In this tutorial, we look at the definition of the exponential function and some of its properties. www.realestate-supersite.com /articles/17/exponential-function-properties.html   (215 words)

 Glossary The period of a function, f, is the length of the shortest interval over which it repeats its values. A function is piecewise-defined, if its rule is given by more than one other formula for different sets of input. A rational function is one whose formula can be given as the ratio (i.e., quotient) of two polynomials. campus.northpark.edu /math/PreCalculus/glossary.html   (1423 words)

 SparkNotes: Exponential and Logarithmic Functions: Exponential Functions An exponential function is a function in which the independent variable is an exponent. Exponential functions have special applications when the base is e. The natural exponential function is especially useful and relevant when it comes to modeling the behavior of systems whose relative growth rate is constant. www.sparknotes.com /math/precalc/exponentialandlogarithmicfunctions/section1.html   (380 words)

 No Title   (Site not responding. Last check: 2007-10-22) Simple exponential functions can always be written as a logarithmic function, where the base of the logarithm is the same as the base of the exponential function. Since the base of the exponential function was e, we can carefully choose a logarithm with base e to isolate the exponent. In this problem, since the base of the exponential function is 5, I carefully chose the logarithm with base 5. www-math.cudenver.edu /~rrosterm/review/review.html   (452 words)

 An Introduction to the Exponential Function   (Site not responding. Last check: 2007-10-22) Exponential equations are the fastest growing functions known in the realm of mathematics today. The limit of this exponential function as x approaches positive infinity is infinity. This asymptote may change depending on the function as shown in the Properties section. www.rose-hulman.edu /Class/FC/HTML/lc/functions/exp/intro.htm   (238 words)

 Exponential Functions   (Site not responding. Last check: 2007-10-22) The graphs of various exponential functions are compared; in addition, a comparison with the graphs of polynomial functions is made. There is an exploration which looks at the approximation of the natural exponential function by polynomials. Use this LiveMath notebook to view an animation showing the graphs of a parametrized family of exponential functions. archives.math.utk.edu /visual.calculus/0/exp_log.5   (285 words)

 Exponential Functions: Introduction Exponential functions look somewhat similar to functions you have seen before, in that they involve exponents, but there is a big difference, in that the variable is now the power, rather than the base. This is the definition of exponential growth: that there is a consistent fixed period during which the function will double (or triple, or quadruple, etc; the point is that the change is always a fixed proportion). Even though the exponential function may start out really, really small, it will eventually overtake the growth of the polynomial, since it doubles all the time. www.purplemath.com /modules/expofcns.htm   (550 words)

 Graphs of Exponential Functions Exponential functions are functions written in the form Using the same values for x, let’s graph this exponential function whose exponent is negative. The graph of this function is decreasing since it begins higher on the left side of the y-axis and continuously decreases in value as it moves toward and crosses over the y-axis. www.algebralab.org /lessons/lesson.aspx?file=Algebra_expfunctions1.xml   (712 words)

 Exponential function The exponential function is the entire function defined by exp(z)=e^z, where e is the constant 2.718... We first start with the properties of the graph of the basic exponential function of base a, f (x) = a x, a > 0 and a not equal to 1. Related: exponential function :: exponential functions :: exponential function graph :: exponential function properties :: exponential function in c :: exponential function derivative :: exponential function calculator :: exponential functions and music :: exponential function c++ :: exponential function rules www.logicjungle.com /wiki/Exponential_function   (327 words)

 SparkNotes: Exponential and Logarithmic Functions: Logarithmic Functions The inverse of the exponential function y = a The domain of a logarithmic function is real numbers greater than zero, and the range is real numbers. The logarithmic function with base 10 is sometimes called the common logarithmic function. www.sparknotes.com /math/precalc/exponentialandlogarithmicfunctions/section2.rhtml   (435 words)

 exponential function - a definition from Whatis.com When the exponent decreases by 1, the value of the function decreases by this same factor (it is divided by e). When the exponent increases by 1, the value of the base-10 function increases by a factor of 10; when the exponent decreases by 1, the value of the function becomes 1/10 as great. For a given, constant base such as e or 10, the exponential function "undoes" the logarithm function, and the logarithm undoes the exponential. whatis.techtarget.com /definition/0,,sid9_gci213699,00.html   (242 words)

 Exponential Functions Exponential functions are explored, interactively, using an applet. The conditions under which an exponential function increases or decreases are also investigated. Use the sliders on the left panel of the applet to set a to 1, b to 1, c to 0, d to 0 and the base B to 2. www.analyzemath.com /expfunction/expfunction.html   (858 words)

 the Exponential function   (Site not responding. Last check: 2007-10-22) The exponential function is singly periodic, with a modulus of periodicity of 2 pi i. Finally, it can be shown that any one of these three properties characterizes the exponential function; that is, any one could be used as the definition, then both of the other two derived from it as theorems. The exponential of a complex x = a + i b (where a and b are real-complex numbers) is www.rism.com /Trig/exponent.htm   (396 words)

 ipedia.com: Exponential function Article   (Site not responding. Last check: 2007-10-22) The exponential function is one of the most important functionss in mathematics. Here, stands for the factorial of n and x can be any real or complex number, or even any element of a Banach algebra or the field of p-adic numbers. To see the equivalence of these definitions, see Definitions of the exponential function. www.ipedia.com /exponential_function.html   (734 words)

 Complex Variables The complex logarithm is the inverse of the complex exponential function. Suppose the complex function f(z) is differentiable on and within a closed curve C in the complex plane, and let R be the region inside the closed curve C. The function f(z) = 1/z is differentiable everywhere in the complex plane except at the point z = 0. www.jgsee.kmutt.ac.th /exell/Numbers/CplxVar.htm   (998 words)

 Transcendental Functions, part 1 We begin by examining the most fundamental of all transcendental functions -- the exponential function. Next consider the graph of the magnitude of the exponential function. The series definition of the exponential function shows that if z = x is real, then the complex exponential function reduces to the real exponential function. www.math.duke.edu /education/ccp/materials/engin/trans/trans1.html   (464 words)

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