Why must b be positive?
Negative bases with non-integer exponents are not always real.
Exponential Function Calculator
Evaluate y = a·b^x or y = e^{kx} for given coefficients and x.
Pick a form and evaluate
Choose a·b^x or e^{kx}, then enter coefficients and x.
About this calculator
How to use Exponential Function Calculator, plus the formulas and logic behind the results.
Tool description
Exponential functions grow or decay by a constant factor. The natural form e^{kx} is the continuous counterpart of compound growth.
How to use
- Select a·b^x or e^{kx}.
- Fill the coefficients used by that mode.
- Enter the evaluation point x.
- Select Calculate to view y.
Formulas & reference
y = a · b^xy = e^{kx}
Checks
- 2 · 3^4 = 162
- e^0 = 1
- b = 1 → constant function y = a
- 0 < b < 1 → decay when a > 0 and x increases
Calculation logic
For a·b^x requires b > 0 (and warns if b = 1 is constant). Uses pow/exp and checks for overflow/NaN.
Base b must be positive for real-valued b^x with arbitrary real x.
Exponential Function Calculator FAQ
Common questions about this calculator and how to use the results.
Is e^{kx} the same as (e^k)^x?
Yes: e^{kx} = (e^k)^x.
Can a be negative?
Yes; it reflects the graph across the x-axis.
What if b = 1?
Then y = a for all x (constant).
How is this different from exponential growth calculator?
This evaluates a function at x; the growth tool projects A₀ over time with rate inputs.
Can x be negative?
Yes. For example 2·3^{−1} = 2/3.