Introduction to Exponential Functions

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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 the base (a positive real number), and 'x' is the exponent.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where 'a' is the initial value, 'b' is the growth factor, and 'x' is the exponent.

Front

How does an exponential function differ from a linear function?

Back

An exponential function grows by a constant factor (multiplication) for each unit increase in x, while a linear function grows by a constant amount (addition).

Front

What does it mean for a function to triple every day?

Back

It means that the function is exponential, specifically of the form f(x) = initial amount * 3^x, where the initial amount is multiplied by 3 for each day.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a * b^x, which determines how much the function increases for each unit increase in x.

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What type of function is represented by a constant addition of values?

Back

A linear function.

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If a function doubles every time, what type of function is it?

Back

It is an exponential function.

Front

What is the value of f(0) in the exponential function f(x) = 2^x?

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f(0) = 2^0 = 1.

Front

What does the graph of an exponential function look like?

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The graph of an exponential function rises rapidly and has a characteristic curve that increases steeply as x increases.

Front

What is the y-intercept of an exponential function?

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The y-intercept is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a * b^x.