Exponential function is one of the basic elementary functions. Generally speaking, the function of y = a x (a is constant and a >；; 0, a≠ 1) is called exponential function, and the definition domain of the function is R. In the definition expression of exponential function, the coefficient before a x must be the number 1, and the independent variable X must be in the position of exponent, and it cannot be other expressions of X, otherwise it is not an exponential function.
Cell division is a very interesting phenomenon, and the speed at which new cells are produced is amazing. For example, when a cell divides, 1 cell splits into two, and two cells split into four ... Therefore, the functional relationship between the new cell number y and the division number x obtained by dividing x is: this function refers to the form of a function, and the independent variable is a power exponent. Let's study such a function.
The general function (a) is a constant, and if a >: 0, a≠ 1) is called an exponential function, the domain of the function is r, and for all exponential functions, the value range is (0, +∞). The previous coefficient in the exponential function is 1. For example, they are all exponential functions; Note: The coefficient before the exponential function is 3, so it is not an exponential function.
Introduction:
Exponential function is an important function in mathematics. This function applied to the value e is written as exp(x). It can also be written as ex, where e is a mathematical constant and the base of natural logarithm, which is about equal to 2.7 1828 1828, also known as Euler number.
When a> is in 1, the negative value of exponential function to x is very flat, and the positive value to x rises rapidly. When x equals 0, y equals 1. When 0
As a function of the real variable x, the image is always positive (above the x axis) and increases (from left to right). It never touches the X axis, although it can be infinitely close to the X axis (therefore, the X axis is the horizontal asymptote of this image. Its inverse function is natural logarithm ln(x), which is defined on all positive numbers X.
Sometimes, especially in science, the term exponential function is more commonly used for functions of the form (k belongs to r), where a is called "radix" and is any positive real number not equal to 1. Firstly, this paper mainly studies the exponential function based on Euler number e.