Exponential function rules are the mathematical guidelines for functions that take the form of f(x) = b^x, where the base is a positive real number. With these functions, the growth rate is proportional to their value.
The exponential parent function is the most basic form of an exponential function. From the general form of an exponential function y = ab^x, an exponential parent function has a value for a equal to one. Therefore, the exponential parent function is written simply as y = b^x.
Exponential functions were created by two men, John Napier and Joost Burgi, independently of each other. Napier was from Scotland, and his work was published in 1614, while Burgi, a native of Switzerland, developed his work in 1620.
To graph exponential functions, create a table of values first, calculating the values for f(x) according to the function given. Each pair of numbers constitutes the coordinates for the points to be drawn on the graph. X will give a coordinate for the x-axis, and f(x) is the coordinate for the y-axi
The pre-exponential factor, or frequency factor, is an aspect of the Arrhenius equation and is related to collision theory. The value for this factor varies depending on the chemical reaction and is determined through experimental observation. However, if values of the rate constant, k, are known at
Transformations of exponential functions occur when the function changes to shift the graph to the left, right, up, down or in reverse. An exponential function can be reversed by adding a negative sign in front of the exponent.
A linear function is graphed as a straight line and contains one independent variable and one dependent variable, whereas an exponential function has a rapid increase or decrease along a curved line in a graph. Linear functions, or equations, take the form "y = a + bx," in which "x" is the dependent
The inverse of an exponential function is a logarithm function. An exponential function written as f(x) = 4^x is read as "four to the x power." Its inverse logarithm function is written as f^-1(y) = log4y and read as "logarithm y to the base four."
"Exponential" is an adjective that means of pertaining to an exponent or exponents, of pertaining to the constant "e," or of an equation having one or more unknown variables in one or more exponents. The word is common in mathematics, and its origins are French and Latin.
Exponential growth and decay can be determined with the following equation: N = (NI)(e^kt). In this equation, "N" refers to the final population, "NI" is the starting population, "t" is the time over which the growth or decay took place and the "k" represents the growth or decay constant. If necessa