AQA A Level Maths: Pure复习笔记6.3.1 Exponential Growth & Decay

Exponential Growth & Decay

What are exponential growth and exponential decay?

  • y = Aekt is exponential growth

6.3.1-Exponential-Growth-Decay-Notes-fig1

  • y = Ae-kt is exponential decay

6.3.1-Exponential-Growth-Decay-Notes-fig2

  • 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 acan be written in the form ekx
    • a= ekx

6.3.1-Exponential-Growth-Decay-Notes-fig3

Will logarithms or ln be involved?

6.3.1-Exponential-Growth-Decay-Notes-fig4

  • ln is the inverse of e

6.3.1-Exponential-Growth-Decay-Notes-fig5

  • The graph of y = ln x is the reflection of the graph of y = ex in the line y = x

Worked Example

6.3.1-Exponential-Growth-Decay-Example-fig1-1

6.3.1-Exponential-Growth-Decay-Example-fig26.3.1-Exponential-Growth-Decay-Example-fig3

 

 

 

 

 

 

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