Exponential Growth & Decay (Edexcel International A Level (IAL) Maths) : Revision Note

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Exponential Growth & Decay

What are exponential growth and exponential decay?

  • y = Aekt is exponential growth

Exponential Growth & Decay Notes fig1, A Level & AS Maths: Pure revision notes
  • y = Ae-kt is exponential decay

 

Exponential Growth & Decay Notes fig2, A Level & AS Maths: Pure revision notes

 

  • k > 0 so plus or minus sign in equation immediately indicates growth or decay

  • A is the starting value or initial value, when t = 0

  • t is often used, rather than x, as many models are time-dependent

Is e always used in exponential growth and decay?

  • Using e makes the maths easier

  • With the proper choice of k, all exponential functions of the form ax can be written in the form ekx

    • ax = ekx

Exponential Growth & Decay Notes fig3, A Level & AS Level Pure Maths Revision Notes

Will logarithms or ln be involved?

Exponential Growth & Decay Notes fig4, A Level & AS Level Pure Maths Revision Notes
  • ln is the inverse of e

Exponential Growth & Decay Notes fig5, A Level & AS Maths: Pure revision notes
  • The graph of y = ln x is the reflection of the graph of y = ex in the line y = x

Worked Example

Exponential Growth & Decay Example fig1, A Level & AS Level Pure Maths Revision Notes
Exponential Growth & Decay Example fig2, A Level & AS Level Pure Maths Revision Notes
Exponential Growth & Decay-Example-fig3, A Level & AS Maths: Pure revision notes
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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.

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