Exponential Growth & Decay (Cambridge (CIE) AS Maths) : Revision Note

Exponential Growth & Decay

What are exponential growth and exponential decay?

• y = Ae^kt 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 a^x can be written in the form e^kx

  • a^x = e^kx

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 y = e^x in the line y = x