Linear vs Exponential Functions

Front

What is an Exponential Function?

Back

A function where the output value increases or decreases at a constant percentage rate, often represented as f(x) = a * b^x, where b is a constant.

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What is a Linear Function?

Back

A function that creates a straight line when graphed, represented as f(x) = mx + b, where m is the slope and b is the y-intercept.

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How do you identify an Exponential Function from a table of values?

Back

Look for a pattern where each y-value is multiplied or divided by the same number as the x-value increases by one.

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How do you identify a Linear Function from a table of values?

Back

Look for a pattern where the difference between consecutive y-values is constant as the x-value increases by one.

Front

What is the general form of an Exponential Growth Function?

Back

f(x) = a * (1 + r)^x, where a is the initial value and r is the growth rate.

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What is the general form of an Exponential Decay Function?

Back

f(x) = a * (1 - r)^x, where a is the initial value and r is the decay rate.

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What does it mean for a function to be linear?

Back

It means that the relationship between the variables can be represented by a straight line, indicating a constant rate of change.

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What does it mean for a function to be exponential?

Back

It means that the relationship between the variables involves a constant percentage change, leading to rapid increases or decreases.

Front

Example of a Linear Function: What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

f(x) = 2x + 3.

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Example of an Exponential Function: What is the equation of an exponential function with a starting value of 5 and a growth rate of 20%?

Back

f(x) = 5 * (1 + 0.2)^x.