• To recognise an exponential function: y = ka bx. • To be able to plot a graph of an exponential function. • To know the properties of exponential functions of the type y = ka bx. • To work with problems of intersecting functions involving an exponential function. • To use exponential functions to solve real-life problems.
19.1 What is an exponential function? Y 10
ACTIVITY ACTION
Plotting exponential functions
OBJECTIVE To rewrite exponential functions in a particular format and to plot their graphs
The mathematics of uncontrolled growth (decay) is frightening. A single bacterium such as an E. coli cell can multiply rapidly (exponentially) under favourable circumstances.
An exponential function is a relation between two variables, x and y, which can be written in the form y = ka bx , where k, a, b are constants with a, b ∈ R, a > 0, k ∈ N.
y = 3 × 2 4x : k = 3, a = 2, b = 4 y = 2 −3x : k = 1, a = 2, b = −3
