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Exponential Graphs Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Exponential graph
A graph where the variable is in the exponent, typically of the form y = a^x.
Shape of exponential growth graph
An upward curve that gets steeper as x increases, starting from a low value.
Shape of exponential decay graph
A downward curve that gets less steep as x increases, approaching zero but never touching it.
Equation of exponential growth
y = a^x, where a > 1.
Equation of exponential decay
y = a^x, where 0 < a < 1.
Key feature of exponential graphs
They have a horizontal asymptote, usually along the x-axis (y = 0).
Effect of increasing 'a' in y = a^x
The graph becomes steeper, showing faster growth or decay.
Exponential graph passing through (0,1)
All exponential graphs of the form y = a^x pass through the point (0,1).
Real-life example of exponential growth
Population growth or compound interest.
Real-life example of exponential decay
Radioactive decay or cooling of an object.
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