Exponential Growth & Decay (CIE A Level Maths: Pure 3)

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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 NotesExponential Growth & Decay-Example-fig3, A Level & AS Maths: Pure revision notes

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Paul

Author: Paul

Expertise: Maths

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 – one of the many reasons he is excited to be a member of the SME team.