Exponential Functions

From compound interest to population growth — observe how the function y = a · bˣ models explosive change in the real world! Explore standard and natural base forms — move the sliders to see how a, b, and c shape the curve.

Active form
Standard form
f(x) = bx
Natural base form
f(x) = ex
a — vertical stretch / reflection 1
b — base (b > 0, b ≠ 1) 2
c — vertical shift / asymptote 0
Parameter effects
y-intercept
(0, 1)
Horizontal asymptote
y = 0
Domain
all real numbers
Range
y > 0
Growth or decay?
growth