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Exponential Function Calculator

Online exponential function calculator: enter the base a and exponent x to evaluate y=a^x. It models doubling growth or decay and is used for compound interest, population growth and radioactive decay.

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y=a^x (a>0,a≠1)
(0,1)
a>0, a≠1
Any real number

📖 Tutorial | Exponential Function

1. Definition
A function y=a^x (a>0, a≠1) is an exponential function, with the exponent x as the variable. It is the inverse of the logarithmic function.
2. Formula & Notation
aConstant base (a>0,a≠1)
xVariable (exponent)
ya^x, always positive
3. Properties & Laws
  • Domain R, range (0,+∞);
  • Passes through (0,1), since a⁰=1;
  • For a>1 it increases (growth);
  • For 0<a<1 it decreases (decay);
  • The line y=0 is the horizontal asymptote.
4. Steps
  1. Enter the base a and exponent x;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: y=2^x at x=3 gives 8; a=1/2 gives 1/8.
6. Common Pitfalls
The base must satisfy a>0 and a≠1;
Values are always positive;
The variable is in the exponent, not the base.

❓ FAQ | Exponential Function

Definition?
y=a^x (a>0,a≠1).
Domain and range?
R and y>0.
Common point?
(0,1).
Growth vs decay?
a>1 grows, 0<a<1 decays.
Vs power function?
The variable is in the exponent.
Asymptote?
y=0 (the x-axis).
Applications?
Interest, population, cell division, decay.