Exponential Growth and Decay

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What is Exponential Growth?

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Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. Example: Population growth where the number doubles at regular intervals.

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What is Exponential Decay?

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Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. Example: Radioactive decay of a substance.

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What is Linear Growth?

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Linear Growth occurs when a quantity increases by a constant amount over equal intervals of time. Example: A person saving a fixed amount of money each month.

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What is Linear Decay?

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Linear Decay occurs when a quantity decreases by a constant amount over equal intervals of time. Example: A car losing a fixed amount of value each year.

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How can you identify Exponential Growth on a graph?

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Exponential Growth is represented by a smooth curve that rises steeply as it moves to the right.

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How can you identify Exponential Decay on a graph?

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Exponential Decay is represented by a smooth curve that falls steeply as it moves to the right.

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What is the difference between Linear and Exponential functions?

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Linear functions increase or decrease at a constant rate, while Exponential functions increase or decrease at a rate proportional to their current value.

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What is the formula for Exponential Growth?

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The formula is: P(t) = P0 * e^(rt), where P0 is the initial amount, r is the growth rate, and t is time.

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What is the formula for Exponential Decay?

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The formula is: P(t) = P0 * e^(-rt), where P0 is the initial amount, r is the decay rate, and t is time.

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What does the 'e' represent in Exponential functions?

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The 'e' is a mathematical constant approximately equal to 2.71828, which is the base of natural logarithms.