Master exponential functions, understand growth and decay, learn transformations, and apply exponential models to real-world problems.
Calculate the value of the exponential expression!
Expression:
Identify if the function represents growth or decay!
Function:
Type:
An exponential function has the form f(x) = a · bˣ, where a is a constant, b > 0 and b ≠ 1 is the base, and x is the exponent.
f(x) = 2ˣ
• Base: 2 (greater than 1, so it's growth)
• f(0) = 2⁰ = 1 (y-intercept)
• f(1) = 2¹ = 2
• f(2) = 2² = 4
• As x increases, f(x) grows rapidly
f(x) = 3 · 2ˣ
• Coefficient: 3
• Base: 2
• f(0) = 3 · 2⁰ = 3 · 1 = 3
• The coefficient affects the y-intercept but not the growth rate