Exponential (Leaving Cert Mathematics): Quizzes

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Exponential
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What is the general form of an exponential function?

f(x)=a⋅bxf(x) = a \cdot b^x

In f(x)=a⋅bxf(x) = a \cdot b^x, what does aa represent?

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

In f(x)=a⋅bxf(x) = a \cdot b^x, what does bb represent?

Base of the exponential function

When does an exponential function represent growth?

When b>1b > 1

When does an exponential function represent decay?

When 0<b<10 < b < 1

Does the function f(x)=0.5(3)xf(x) = 0.5(3)^x represent growth or decay?

Growth

Does the function f(x)=0.5(0.1)xf(x) = 0.5(0.1)^x represent growth or decay?

Decay

What is the y-intercept of f(x)=0.5(3)xf(x) = 0.5(3)^x?

0.50.5

Which point does the graph of f(x)=a⋅bxf(x) = a \cdot b^x always pass through?

(0,a)(0, a)

How does an exponential decay graph behave as xx increases?

Decreases rapidly

In exponential decay, does the graph ever reach zero?

No, never

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