5.3 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 in the total amount.

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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 in the total amount.

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How do you identify an exponential growth model?

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An exponential growth model can be identified by a positive growth rate (percentage) and a function of the form y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

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How do you identify an exponential decay model?

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An exponential decay model can be identified by a negative growth rate (percentage) and a function of the form y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

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What is the formula for calculating the future value in an exponential growth scenario?

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The future value can be calculated using the formula: FV = P(1 + r)^t, where FV is the future value, P is the principal amount, r is the growth rate, and t is the time in years.

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What is the formula for calculating the future value in an exponential decay scenario?

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The future value can be calculated using the formula: FV = P(1 - r)^t, where FV is the future value, P is the principal amount, r is the decay rate, and t is the time in years.

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What does the term 'initial amount' refer to in exponential models?

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The initial amount refers to the starting quantity before any growth or decay has occurred.

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How do you calculate the multiplier for exponential decay?

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The multiplier for exponential decay is calculated as 1 minus the decay rate (expressed as a decimal). For example, if the decay rate is 30%, the multiplier is 1 - 0.30 = 0.70.

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What is the significance of the growth rate in exponential models?

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The growth rate determines how quickly the quantity will increase or decrease over time, significantly affecting the outcome of the model.

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How can you model a population that grows by a certain percentage each month?

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You can model the population growth using the formula: P(t) = P0(1 + r)^t, where P0 is the initial population, r is the monthly growth rate, and t is the number of months.