In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718) such that the function ex equals its own derivative.[1][2] The exponential function is used to model phenomena when a constant change in the independent variable gives the same proportional change (increase or decrease) in the dependent variable. The exponential function is also often written as exp(x), especially when x is an expression complicated enough to make typesetting it as an exponent unwieldy.
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 graph at each point is equal to its y co-ordinate at that point. The inverse function is the natural logarithm ln(x); because of this, some older sources refer to the exponential function as the anti-logarithm.
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.
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Jones
Sat, 22 Aug 2009 18:36:40 GM
Hi, I need to find all z~~\text{such that}~~ e^{z} So let z =a+bi then e^{a}*e^{bi} Now we can write this as e^{a}*(cos(b) + i sin(b Also i know that the modulus is \sqrt{2} But that's about it really..
