Exponential-Growth-And-Decay Aqa Higher

Exponential growth & decay

What is exponential growth?

• When a quantity grows exponentially it is increasing from an original amount by a percentage each year for years

  • Some questions use a different timescale, such as each day, or each minute

• Real-life examples of exponential growth include:

  • Population increases

  • Bacterial growth

  • The number of people infected by a virus

What is exponential decay?

• When a quantity exponentially decays it is decreasing from an original amount by a percentage each year for years

  • Some questions use a different timescale, such as each day, or each minute

• Real-life examples of exponential decay include:

  • The temperature of hot water cooling down

  • The value of a car decreasing over time

  • Radioactive decay (the mass of a radioactive a substance over time)

How can I model a scenario as exponential growth or decay?

• Scenarios which exponentially grow or decay can be modelled with an equation

• A useful format for this equation is

  • where:

    • is the starting (initial) amount

    • is the new amount

    • is the appropriate multiplier or scale factor for the growth or decay in the time period

      • E.g. for a 20% decay, for a 20% growth

    • is the number of time periods

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