Exponential Mathematics Formula with example

Maths Formulas

Exponential Mathematics Formula

Write an Exponential FunctionExponential Mathematics Formula with exampleis defined as the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. so

The exponential function is the important mathematical function which is of the form then

f(x) = ax

Where a>0 and a is not equal to 1. so

x is any real number.

If ta variable is negative, the function is undefined for -1 < x < 1. so

Here,

“x” can be a variable

“a” is the constant, which is the base of the function.

The exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by the fixed per cent at regular intervals should possess either exponential growth or exponential decay. so

Exponential Mathematics Formula with example

Exponential Mathematics Formula

Which of the following equations are not exponential functions?

  • f(x)=43(x2)f(x)=43(x−2)
  • g(x)=x3g(x)=x3
  • h(x)=(13)xh(x)=(13)x
  • j(x)=(2)xj(x)=(−2)x

Solution

By definition, an exponential function has a constant as a base and an independent variable as an exponent. Thus, g(x)=x3g(x)=x3 does not represent an exponential function because the base is an independent variable. In fact, g(x)=x3g(x)=x3 is a power function. so

Recall that the base bb of an exponential function is always a positive constant, and b1b≠1. Thus, j(x)=(2)xj(x)=(−2)x does not represent an exponential function because the base, 2−2, is less than 00. so

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