Exponential Function Definition Exponential Function Definition In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. The function is often written as exp(x), especially when it is impractical to write the independent variable as a superscript. The exponential function is widely used in physics, chemistry and mathematics. The graph of y = ex is upward-sloping, and increases faster as x increases. The graph always lies above the x-axis but can get arbitrarily close to it for negative x; thus, the x-axis is a horizontal asymptote. The slope of the tangent to the graph at each point is equal to its y coordinate at that point. The inverse function is the natural logarithm ln(x); because of this, some old texts refer to the exponential function as the antilogarithm.
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Sometimes the term exponential function is used more generally for functions of the form cbx, where the base b is any positive real number, not necessarily e. See exponential growth for this usage. In general, the variable x can be any real or complex number, or even an entirely different kind of mathematical object; see the formal definition below. We generally study different type of Functions in the Math like the Trigonometric Functions which include the sine function, the cosine function, the Tangent function, the log function, the greatest Integer function, etc. One of such functions of the math which is the most common function is exponential function. The exponential function in the context of the math is a function which is represented by ex in which ‘e’ denotes a number whose value is approximately equal to 2.718281828. This function is such type of the function which has the same derivative as itself that is the derivative is also equal to ex. Exponential functions are generally utilized in the modeling of a kind of the relationship where a constant variation in the variable which is independent produces an equally proportional variation in the variable which is dependent that is it produces an equally proportional increase or the decrease when it is considered percent wise. This function is generally written in the form exp ( x ) and specially during the conditions when it is not practical to write the variable which is independent in the form of a superscript. The inverse of these functions are called as the log functions.
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Now, let us discuss something about the graph of these functions. The graph of function y = ex is of sloping type which is sloping in the upward direction and also the graph of this function increases very rapidly with the increase in the value of the x. The graph of exponential exists always on the upper side of the x axis and gets close to the x axis for those values of the x which are negative. Hence we can say that the x axis can be called as the horizontal Asymptote of the function.
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