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

What are exponential growth and exponential decay?

• y = Aekt is exponential growth

• y = Ae-kt is exponential decay

• 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
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Will logarithms or ln be involved?

• ln is the inverse of e

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