Exponential Graphs (HSC SSCE Mathematics Advanced): Flashcards

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Exponential Graphs
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General form of exponential function

y=axy = a^x, where variable is in exponent and a>0a > 0

Exponential growth definition

Quantity increases at rate proportional to current value

Exponential decay definition

Quantity decreases at rate proportional to current value

Asymptote definition

Line that curve approaches but never actually touches

Y-intercept of y=k(ax)y = k(a^x)

(0,k)(0, k)

Horizontal asymptote of y=k(ax)y = k(a^x)

y=0y = 0

Base aa condition for exponential growth

a>1a > 1

Base aa condition for exponential decay

0<a<10 < a < 1

Domain of exponential functions

All real numbers

Range of y=k(ax)y = k(a^x) when k>0k > 0

y>0y > 0

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