What does y = a·b^x mean?
Starting from a, you multiply by the base b once for every step in x. With a = 2 and b = 3, x = 4 gives 2 × 3 × 3 × 3 × 3 = 162.
// maths › Algebra
Exponential calculator
Evaluate y = a·b^x at a chosen x, with the growth/decay curve plotted.
y = a · b^x
Frequently asked questions
What is the difference between growth and decay?
If the base is greater than 1 the curve rises (growth); if the base is between 0 and 1 it falls toward zero (decay).
How is this different from a linear equation?
A line adds the same amount each step; an exponential multiplies by the same factor each step, so it changes far faster as x grows.
Where is this used in real life?
Populations — bacteria doubling each hour follow b = 2. Radioactive decay and medicine half-lives use a base between 0 and 1. Money — compound interest is exponential growth. Epidemics — early case counts often grow exponentially, which is why they rise so suddenly.
What do the dots on the graph mean?
Each dot marks an integer power (b⁰, b¹, b², …). Reading them left to right shows the value multiplying by the base at every step.