Ch.5 Flashcard#2 Exponential Decay

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What is Exponential Decay?

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Exponential decay is a process where a quantity decreases at a rate proportional to its current value, often represented by the formula y = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

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What is the decay rate in exponential decay?

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The decay rate is a constant that represents the fraction of the quantity that decreases over a specific time period. It is typically a small positive number.

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What does a decay rate of 0.001 indicate?

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A decay rate of 0.001 means that 0.1% of the quantity remains after each time period, indicating a slow decay.

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What is the initial amount in exponential decay?

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The initial amount is the value of the quantity at time t=0, often denoted as 'a' in the exponential decay formula.

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How can you identify exponential decay on a graph?

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Exponential decay is identified on a graph as a curve that decreases rapidly at first and then levels off, approaching zero but never actually reaching it.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when a quantity decreases at a rate proportional to its current value.

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What does the graph of exponential growth look like?

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The graph of exponential growth shows a curve that rises steeply, indicating that the quantity increases rapidly over time.

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What is the formula for exponential decay?

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The formula for exponential decay is y = a * e^(-kt), where 'y' is the quantity at time 't', 'a' is the initial amount, 'k' is the decay constant, and 'e' is the base of the natural logarithm.

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What is the significance of the decay constant 'k'?

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The decay constant 'k' determines the rate of decay; a larger 'k' value indicates a faster decay.

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How do you calculate the remaining amount after a certain time in exponential decay?

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To calculate the remaining amount, use the formula y = a * e^(-kt), substituting 'a' for the initial amount, 'k' for the decay constant, and 't' for the time elapsed.