Exponential Function formula

About Exponential Function formula

What is the meaning of the exponential function?

An exponential function is a mathematical function of form f (x) = ax, where "x" is a variable and "a" is a constant that is the function's base and must be greater than 0. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis. Get the list of Maths Formulas. 

The formula for Exponential Functions

The exponential function is defined by the formula f(x) = ax, where x represents an exponent in the input variable. The exponential curve is determined by the exponential function and the value of x.

The exponential function, which has the form f(x) = ax, is an important mathematical function.

Where a>0, a is not equal to 1,x is any real number.

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

Here, “x” is a variable and “a” is a constant, which is the base of the function.

The exponential function determines whether an exponential curve grows or decays. Either exponential growth or exponential decay should be present in any quantity that grows or decays by a defined percentage at regular intervals.

Exponential Growth

The quantity increases extremely slowly at first, then rapidly in exponential growth. Over time, the rate of change accelerates. With time, the rate of growth accelerates. The quick expansion is described as an "exponential increase." The exponential growth formula is as follows y = a(1 + r)x Here r is the growth percentage.

Exponential Function Rules

The following are some important exponential rules:

  1. For any real numbers x and y, if a>0 and b>0, the following is true:
  2. ax ay = ax+y
  3. ax/ay = ax-y
  4. (ax)y = axy
  5. axbx = (ab)x
  6. (a/b)x= ax/bx
  7. a0 = 1
  8. a-x = 1/ax
  9. Examples of Exponential Functions
  10. The following are some instances of exponential functions:
  11. f(x) = 2x
  12. f(x) = 1/2x= 2-x
  13. f(x) = 2x+ 3
  14. f(x) = 0.5x

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Exponential Function formula
Exponential Function formula

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