Linear or Exponential?

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What is a linear function?

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A linear function is a function that graphs to a straight line. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is an exponential function?

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An exponential function is a function in which an independent variable appears in the exponent. It can be expressed in the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

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How can you identify a linear relationship in data?

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A linear relationship can be identified if the data points form a straight line when graphed, indicating a constant rate of change.

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How can you identify an exponential relationship in data?

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An exponential relationship can be identified if the data points form a curve that increases or decreases rapidly, indicating a variable rate of change.

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What does it mean for a function to exhibit linear growth?

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Linear growth means that the function increases by the same amount over equal intervals. For example, if a function increases by 5 units for every 1 unit increase in x, it exhibits linear growth.

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What does it mean for a function to exhibit exponential growth?

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Exponential growth means that the function increases by a percentage of its current value over equal intervals. For example, if a function doubles every time x increases by 1, it exhibits exponential growth.

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What is the slope of a linear function?

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The slope of a linear function is the ratio of the change in y to the change in x (rise over run). It indicates how steep the line is.

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What is the y-intercept of a linear function?

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The y-intercept of a linear function is the point where the line crosses the y-axis. It is the value of y when x = 0.

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What is a real-world example of linear growth?

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A real-world example of linear growth is a fixed monthly subscription fee, such as a smartphone data plan that charges a constant amount each month.

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What is a real-world example of exponential growth?

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A real-world example of exponential growth is the population of bacteria that doubles every hour under ideal conditions.