Exponential Functions (AQA A-Level Mathematics): Flashcards

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Exponential Functions
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General form of exponential function

y=abxy = a \cdot b^x

Condition for exponential growth (value of bb)

b>1b > 1

Condition for exponential decay (value of bb)

0<b<10 < b < 1

Domain of exponential functions

All real numbers (xRx \in \mathbb{R})

Y-intercept of y=abxy = a \cdot b^x

y=ay = a

Approximate value of natural base ee

2.7182.718

Natural exponential function formula

y=exy = e^x

Horizontal asymptote of exponential function

Usually at y=0y = 0 (the x-axis)

Exponential growth model formula

y=y0ekty = y_0 \cdot e^{kt} where k>0k > 0

Exponential decay model formula

y=y0ekty = y_0 \cdot e^{-kt} where k>0k > 0

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