Exponential growth and decay (HSC SSCE Mathematics Extension 1): Flashcards

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Exponential Growth and Decay
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What is exponential growth?

Growth based on the current size continuously.

What is exponential decay?

Decrease based on the current size continuously.

What is the formula for exponential growth?

y = A e^{kx}

What is the formula for exponential decay?

y = A e^{-kx}

How does compound interest relate to growth?

It grows continuously based on the current amount.

What is a common mistake in growth vs decay?

Confusing growth and decay factors in derivations.

What is half-life in radioactive decay?

Time taken for half the substance to decay.

What is Newton's Law of Cooling?

Describes temperature drop using decay principles.

How do you derive the growth formula?

Separate variables and integrate dy/y = k dx.

What do exponential graphs show?

Differences in growth rates compared to linear functions.

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