What is e, the exponential function?
- The exponential function is y = ex
- e is an irrational number
- e ≈ 2.718
- As with other exponential graphs y = ex
- passes through (0, 1)
- has the x-axis as an asymptote
What is the big deal with e?
- y = ex has the particular property
- ie for every real number x, the gradient of y = ex is also equal to ex (see Derivatives of Exponential Functions)
The negative exponential graph
- y = e-x is a reflection in the y-axis of y = ex
- They are of the form y = f(x) and y = f(-x) (see Transformations of Functions - Reflections)
What is exponential growth and decay?
- y = Aekx (k > 0) is exponential growth
- y = Ae-kx (k > 0) is exponential decay
- A is the initial value
- k is a (usually positive) constant
- “-“ is used in the equation making clear whether it is growth or decay