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
- ax = ekx
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 = ex in the line y = x