Here are some:
* They tend to grow (or decrease) very fast* The derivative of the basic exponential function is equal to the function value itself
* They are used to describe many common situations, such as the growth of a population under certain conditions, radioactive decay, etc.
* An exponential function with a positive exponent will eventually grow faster than any polynomial function
The gradient at any point is directly proportional to the value of the function at that point.
Do you mean "equations involving exponential functions"? Yes,
chicken
Trigonometric functions, exponential functions are two common examples.
The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field. Each one of the functions can be defined for a complex variable.
There are several laws of exponential functions, not just one. Here is just one of them:The derivative of THE exponential function (base e) is the same as the function itself.
Exponential and logarithmic functions are inverses of each other.
There are no points of discontinuity for exponential functions since the domain of the general exponential function consists of all real values!
Exponential and logarithmic functions are different in so far as each is interchangeable with the other depending on how the numbers in a problem are expressed. It is simple to translate exponential equations into logarithmic functions with the aid of certain principles.
Do you mean "equations involving exponential functions"? Yes,
Yes.
chicken
Trigonometric functions, exponential functions are two common examples.
The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field. Each one of the functions can be defined for a complex variable.
M. I. Liechenstein has written: 'Two-parameter exponential and rational functions for least-square approximations' -- subject(s): Approximation theory, Exponential functions, Least squares 'Orthonormal bases for exponential and rational function approximations of network and signal characteristics' -- subject(s): Exponential functions, System analysis 'Designing for security' -- subject(s): Security systems 'Reducing crime in apartment dwellings' -- subject(s): Apartment houses, Security measures 'Delay distortion and signal impairment in digital data transmission' -- subject(s): Data transmission systems
There are several laws of exponential functions, not just one. Here is just one of them:The derivative of THE exponential function (base e) is the same as the function itself.
They have infinite domains and are monotonic.
They are inverses of each other.