Exponential+Functions+Review

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=Exceedingly Excellent Exponential Functions=

Defining an Exponential Function

 * An exponential function can be defined as a function of the form //ka//×
 * //a//, called the //base//, is any positive real number not equal to one
 * x, which can be any real or complex number, is the independent variable of the function
 * k is the function's constant value
 *  //Ex: g//(//x//) = 2 ×, where the base (2) is the fixed number, and the power (x) is the variable.

Euler's Number

 * the form //e//×, where //**e**// is a mathematical constant, the base of the natural logarithm, which equals approximately 2.718281828, and is also known as Euler's number
 * As a function of the //real// variable //x//, the graph of //y//=//e//× is always positive (above the //x// axis) and increasing (viewed left-to-right). It never touches the //x// axis, although it gets arbitrarily close to it (thus, the //x// axis is a horizontal asymptote to the graph). Its inverse function, the natural logarithm, ln(//x//), is defined for all positive //x//.

Uses of Exponential Functions

 * Exponential functions are used to model changes in population size, in the spread of diseases, and in 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 //e//×, the inverse of the natural logarithmic function.

Examples of Exponential Funtions
(ADD: various graphs of common exponential funtions, with large and small ind. vars.)

