Graphs of Practical Situations (HSC SSCE Mathematics Standard): Flashcards

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Exponential Functions and Models
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Practise the cards

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Variable position in exponential function

In the exponent (power)

General forms of exponential functions

y=axy = a^x and y=axy = a^{-x} where a>0a > 0

Y-intercept of all exponential graphs

(0, 1)

Output values of exponential functions

Always positive (above x-axis)

Asymptote for exponential graphs

The x-axis

Growth function form (when a>1a > 1)

y=axy = a^x (y increases as x increases)

Decay function form (when a>1a > 1)

y=axy = a^{-x} (y decreases as x increases)

Relationship between y=axy = a^x and y=axy = a^{-x} graphs

Reflection in the y-axis

Examples of exponential growth models

Population, compound interest, disease spread, tech adoption

Examples of exponential decay models

Radioactive decay, depreciation, medication, cooling

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