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An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3 x = 81, 5 x - 3 = 625, 6 2y - 7 = 121, etc are some examples of exponential equations.
By definition, an exponential function has a constant as a base and an independent variable as an exponent. Thus, \(g(x)=x^3\) does not represent an exponential function because the base is an independent variable.
What is an exponential function? An exponential function is a mathematical function in the form y=abx, y = abx, where x x and y y are variables, and a a and b b are constants, b>0. b> 0. For example, The diagram shows the graphs of y=2x,y=0.4x, y = 2x,y = 0.4x, and y=0.5(3x). y = 0.5(3x).
Finding Equations of Exponential Functions. In the previous examples, we were given an exponential function, which we then evaluated for a given input. Sometimes we are given information about an exponential function without knowing the function explicitly.
An exponential equation is a mathematical equation in which the unknown variable appears in the exponent. Exponential equations can also take various forms, such as exponential growth or decay equations, continuous exponential functions, and equations involving initial values.
When populations grow rapidly, we often say that the growth is “exponential,” meaning that something is growing very rapidly. To a mathematician, however, the term exponential growth has a very specific meaning. In this section, we will take a look at exponential functions, which model this kind of rapid growth.
Definition. Exponential equations are mathematical expressions where the unknown variable appears as the exponent. These equations describe situations where a quantity grows or decays at a constant rate over time, and they are commonly used to model real-world phenomena such as population growth, radioactive decay, and compound interest.
We will cover the basic definition of an exponential function, the natural exponential function, i.e. e^x, as well as the properties and graphs of exponential functions.
The meaning of EXPONENTIAL EQUATION is an equation involving exponential functions of a variable.
Let’s start off this section with the definition of an exponential function. If b b is any number such that b> 0 b> 0 and b ≠ 1 b ≠ 1 then an exponential function is a function in the form, where b b is called the base and x x can be any real number. Notice that the x x is now in the exponent and the base is a fixed number.