Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

How do you identify an exponential growth graph?

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An exponential growth graph rises steeply as x increases, showing a J-shaped curve.

Front

How do you identify an exponential decay graph?

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An exponential decay graph falls steeply as x increases, approaching the x-axis but never touching it.

Front

What is the y-intercept of an exponential function?

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The y-intercept is the initial value of the function, found by evaluating f(0). For f(x) = a(b^x), it is 'a'.

Front

If a function has a base greater than 1, what type of function is it?

Back

It is an exponential growth function.

Front

If a function has a base between 0 and 1, what type of function is it?

Back

It is an exponential decay function.

Front

What does the term 'initial value' refer to in an exponential function?

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The initial value is the starting amount of the quantity before any growth or decay occurs, represented by 'a' in f(x) = a(b^x).