Calculate the value of an exponential function in the form f(x) = a · bˣ.
Last updated: March 2026 | By ForgeCalc Engineering
An exponential function is a mathematical function of the form $f(x) = a \cdot b^x$, where $a$ is the initial value, $b$ is a positive constant called the base, and $x$ is the exponent.
Unlike linear functions which grow by a constant amount, exponential functions grow (or decay) by a constant percentage. This leads to extremely rapid changes as $x$ increases.
a: Initial value (y-intercept)
b: Growth factor (base)
x: Input variable (exponent)
Evaluate f(x) = 3 · 2ˣ for x = 4:
1. Identify a = 3, b = 2, x = 4
2. Calculate 2⁴: 2 * 2 * 2 * 2 = 16
3. Multiply by a: 3 * 16 = 48
Final Answer: 48
The function represents exponential decay. The values will get smaller as x increases.
The function becomes a constant f(x) = a, because 1 to any power is 1.
Yes. If a is negative, the graph is reflected across the x-axis.
They model population growth, radioactive decay, compound interest, and the spread of viruses.
The horizontal asymptote is at y = 0. As x approaches negative or positive infinity (depending on b), the function approaches 0 but never reaches it.
The parameter 'a' is the y-intercept (when x = 0, f(0) = a). It stretches or shrinks the graph vertically without changing the base exponential behavior.
The domain (all possible x values) is all real numbers. The range (all possible y values) depends on the sign of 'a': if a > 0, range is (0, ∞); if a less than 0, range is (-∞, 0).
Logarithms are the inverse of exponential functions. If f(x) = b^x, then the inverse function is log_b(x). They 'undo' each other.
Related Tools