Exponential Growth & Decay (Cambridge (CIE) IGCSE Maths)

Exponential Growth & Decay

The ideas of compound interest and depreciation can be applied to other (non-money) situations, such as increasing or decreasing populations.

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

  • Note if then it is exponential growth

    • If then it is exponential decay

    • cannot be negative

How do I use the exponential growth & decay equation?

• You may need to rearrange the equation

  • To find giving

  • To find giving so

  • To find , using trial and improvement

    • Test different whole-number values for until both sides of the equation balance

How does exponential growth and decay relate to exponential graphs?

• Plotting the exponential model on a graph where:

  • is on the x-axis

  • and is on the y-axis

  • gives the shape of an exponential graph

    • often written as