Exponential Functions Flashcards

Grade 10 · Math · Flashcards

Key terms, properties, and formulas for exponential functions.

Flashcards

Exponential function: f(x) = a·bˣ where b > 0, b ≠ 1; variable is in the exponent
Base b > 1: Exponential growth — output increases as x increases
Base 0 < b < 1: Exponential decay — output decreases toward zero as x increases
Initial value (a): The y-intercept; f(0) = a since b⁰ = 1
Horizontal asymptote: y = 0 for f(x) = a·bˣ; shifts to y = k when f(x) = a·bˣ + k
Natural base e: ≈ 2.71828; appears in continuous growth/decay models
Continuous growth formula: A = Peʳᵗ where P=principal, r=rate, t=time
Compound interest formula: A = P(1 + r/n)^(nt) where n = compounding periods per year
Growth factor: b in f(x) = a·bˣ; the amount multiplied each period
Decay factor: b in decay model where 0 < b < 1; percent retained = b × 100%
Percent decrease → decay factor: If depreciating by r%, the factor is (1 - r/100)
Domain of f(x) = a·bˣ: All real numbers (−∞, ∞)
Range of f(x) = a·bˣ (a > 0): All positive reals (0, ∞); never equals zero
Reflection across y-axis: f(-x) = a·b⁻ˣ = a·(1/b)ˣ; growth becomes decay and vice versa