FUN015 · Functions & graphs · Classes 10–12
Exponential Function
An exponential function has the variable in the exponent. With a > 1 it grows, with 0 < a < 1 it decays, and it always passes through (0, 1).
aˣExponential Function
📐 Formula
f(x) = aˣ, a > 0; asymptote y = 0
✏️ Worked example
a = 2: f(3) = 2³ = 8 and f(0) = 1.
🌍 Where it is used
Compound interest, bacteria growth and cooling.
❓ Quick check
Every graph y = aˣ passes through…
🏋️ Practice
EasyFor f(x) = 3ˣ, find f(2).
Answer: 9
MediumFor f(x) = 2ˣ, find f(−1).
Answer: 1/2
ChallengeIs y = (1/2)ˣ growth or decay?
Answer: Decay