Exponential Function Explorer

Visualize and calculate exponential functions of the form $$f(x) = a \cdot b^x$$.

Enter values for a, b, and x to explore!

Exponent x

x =

Coefficient a

a =

Base b

b =

$$f(x) =$$

Understanding Exponential Functions

Exponential functions are powerful tools for modeling situations with rapid growth or decay. The general form is $$f(x) = a \cdot b^x$$, where:

a is the coefficient, scaling the function vertically. It represents the initial value when x=0.
b is the base, determining the rate of change.
- If b > 1, the function shows exponential growth.
- If 0 < b < 1, it shows exponential decay.
x is the exponent, the variable in the function.

Use this calculator to explore how changing a, b, and x affects the function and its graph. Visualize the curve to understand exponential behavior.

Population Growth: If a population grows at a rate of 5% per year, the growth can be modeled by an exponential function with b = 1.05.
Radioactive Decay: The decay of radioactive substances is modeled by exponential decay, where 'b' is less than 1.
Compound Interest: The amount of money after compound interest is calculated using an exponential function.