Exponential Growth Wins
Aligned to F-LE.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
A quantity growing exponentially will eventually overtake any quantity growing linearly, quadratically, or as a polynomial, no matter how large the other one starts. The repeated multiplying compounds quickly.
Worked example
Compare f(x) = 2^x and g(x) = 10x. At x = 4, f = 16 and g = 40, so g leads. But at x = 7, f = 128 and g = 70 — the exponential has passed the linear.
Practice questions
- Compare 2^x and 5x at x = 5.
- Which is larger at x = 10: 2^x or x^2?
- Explain in words why doubling beats adding a fixed amount over time.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
El Crecimiento Exponencial Gana
Una cantidad que crece de forma exponencial terminará por superar a cualquier cantidad que crezca de forma lineal, cuadrática o polinomial, sin importar qué tan grande empiece la otra. La multiplicación repetida se acumula rápido.
Ejemplo: Compara f(x) = 2^x y g(x) = 10x. En x = 4, f = 16 y g = 40, así que g va adelante. Pero en x = 7, f = 128 y g = 70: la exponencial ya pasó a la lineal.
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