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, represented by the function f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

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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, represented by the function f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

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What does the initial amount represent in an exponential function?

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The initial amount is the value of the function when x = 0, representing the starting quantity before any growth or decay occurs.

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How do you identify exponential growth from a function?

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Exponential growth can be identified if the base of the exponent is greater than 1 (e.g., f(x) = a(1 + r)^x).

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How do you identify exponential decay from a function?

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Exponential decay can be identified if the base of the exponent is between 0 and 1 (e.g., f(x) = a(1 - r)^x).

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What is the formula for exponential growth?

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

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What is the formula for exponential decay?

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

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If a population doubles every 3 years, what type of growth is this?

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This is an example of exponential growth.

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What is the decay rate if a substance reduces to half its amount in 5 hours?

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The decay rate can be calculated using the formula for exponential decay, where the half-life is the time taken to reduce to half.

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How do you convert a percentage growth rate to a decimal for use in exponential functions?

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To convert a percentage growth rate to a decimal, divide the percentage by 100 (e.g., 35% becomes 0.35).