Exponential (Leaving Cert Mathematics): Flashcards

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Exponential
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General form of exponential function

f(x)=a⋅bxf(x) = a \cdot b^x

Meaning of aa in f(x)=a⋅bxf(x) = a \cdot b^x

Initial value (y-intercept when x=0x=0)

Meaning of bb in f(x)=a⋅bxf(x) = a \cdot b^x

Base of exponential function

Condition for exponential growth

b>1b > 1

Condition for exponential decay

0<b<10 < b < 1

Point all exponential graphs pass through

(0,a)(0, a)

Why exponential graphs pass through (0,a)(0, a)

Because b0=1b^0 = 1

Exponential decay behaviour as xx increases

Decreases rapidly but never reaches zero

Does exponential decay ever reach zero?

No, never actually reaches zero

Meaning of xx in f(x)=a⋅bxf(x) = a \cdot b^x

Independent variable

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