Advanced MathHard
Nonlinear functions
Understand exponential, quadratic, and other nonlinear functions including their graphs, key features, and real-world applications.
Sample SAT Problem
A population doubles every 3 years. If it starts at 500, what is it after 9 years?
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Step-by-Step Solution
After 9 years = 3 doublings: 500 × 2³ = 500 × 8 = 4,000.
Key Tips from Pamela
- Vertex form y = a(x − h)² + k gives you the vertex directly.
- Exponential growth: y = a(1 + r)ˣ; decay: y = a(1 − r)ˣ.
- The axis of symmetry of a parabola is x = −b/(2a).
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