Exponential Function Calculator

Evaluate any exponential function f(x) = a·bx for a given x, see the curve graphed with the point marked, and find out whether it models growth or decay — with every step shown.

f(x) =
· x
x =
Your function
Result —

How to Evaluate an Exponential Function

Enter a coefficient, a base, and a value of x to see the result and the working.

1

Enter a, b, and x

Type the starting value a, the base b, and the value of x you want to evaluate at — for example a = 1, b = 2, x = 3 for 23. Type e in the base field for the natural exponential (base e ≈ 2.71828).

2

The calculator raises b to the power x

It computes bx, multiplies by the coefficient a, and classifies the curve — growth when b > 1, decay when 0 < b < 1 — showing each step so you can follow the working.

3

Read the result and the graph

The value f(x) appears at the top, the curve is plotted with your point marked, and the y-intercept and steps are listed below. Going the other way? The Log Calculator is the inverse of the exponential, and the Derivative Calculator handles rates of change.

Frequently Asked Questions

What is an exponential function?
An exponential function has the form f(x) = a·bx, where the variable x sits in the exponent, b > 0 is the base, and a is the starting value (the y-intercept, because b0 = 1 so f(0) = a). Unlike a power function such as x2, where the base changes and the exponent is fixed, here the exponent changes and the base stays constant. This is what produces the characteristic runaway growth of compound interest, populations, and chain reactions, or the steady decay of radioactive material and cooling objects.
What is the difference between exponential growth and decay?
It depends entirely on the base b. When b > 1 the function grows — each step in x multiplies the output by b, so the curve rises ever more steeply to the right (exponential growth). When 0 < b < 1 the function shrinks — each step multiplies by a fraction, so the curve falls toward the x-axis without ever touching it (exponential decay). When b = 1 the output never changes, so f(x) = a is just a constant. This calculator labels which case you are in as you type.
How do you calculate ex?
ex is the exponential function with base e ≈ 2.71828, the natural exponential. To evaluate it at a value, raise e to that power: e2 = 2.718282 ≈ 7.389, e0 = 1, and e−1 = 1/e ≈ 0.368. Type e in the base field and enter your x value — the calculator computes e raised to that power and plots the curve. ex is special because it is its own derivative, which is why it appears throughout calculus, growth models, and probability.
Why does the exponential curve never touch the x-axis?
Because a positive base raised to any real power is always positive — it can get arbitrarily close to zero but never reach it. So for f(x) = a·bx with a positive a, the line y = 0 is a horizontal asymptote: as x heads toward negative infinity (for growth) the curve flattens toward the x-axis but stays above it forever. That is the mirror image of why logarithms are only defined for positive inputs, since the logarithm is the inverse of the exponential.