Exponential Growth or 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. For example, if a population grows by 10% each year, it will grow faster each subsequent year.

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What is exponential decay?

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Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. For example, if a substance loses 5% of its mass each year, it will lose more mass each subsequent year.

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What is the general formula for exponential growth?

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The general formula for exponential growth is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

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What is the general formula for exponential decay?

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The general formula for exponential decay is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

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How do you identify exponential growth from a graph?

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Exponential growth graphs show a J-shaped curve that rises steeply as x increases, indicating that the quantity is increasing rapidly.

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How do you identify exponential decay from a graph?

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Exponential decay graphs show a curve that decreases rapidly at first and then levels off, indicating that the quantity is decreasing over time.

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What does a growth rate of 35% mean in an exponential function?

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A growth rate of 35% means that the quantity increases by 35% of its current value each time period.

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If a function is represented as y = 15(1.35)^x, what does '15' represent?

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'15' represents the initial amount or starting value before any growth occurs.

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What is the difference between linear growth and exponential growth?

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Linear growth increases by a constant amount each time period, while exponential growth increases by a percentage of the current value, leading to faster increases over time.

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What is the significance of the base in an exponential function?

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The base of an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.