Identify Linear v Exponential Functions

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What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

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What is an exponential function?

Back

An exponential function is a function in which an independent variable is in the exponent. It can be represented by the equation 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 function from a word problem?

Back

A linear function can be identified by a constant rate of change, such as a fixed amount added or subtracted over time.

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How can you identify an exponential function from a word problem?

Back

An exponential function can be identified by a situation where the quantity increases or decreases by a percentage or factor over time.

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What is the equation for a linear function that starts at 8000 and adds 500 each year?

Back

y = 500x + 8000

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What is the equation for an exponential function that starts at 20000 and halves every decade?

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y = 20000(0.5)^(x/10) where x is the number of years.

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If a stock increases by $2 every day, what type of function does this represent?

Back

This represents a linear function.

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If a gym charges a membership fee plus a fee per visit, what type of function does this represent?

Back

This represents a linear function.

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What does the slope represent in a linear function?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

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What does the base represent in an exponential function?

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The base represents the growth or decay factor in an exponential function, indicating how much the quantity multiplies or divides over each time period.