is continuous, always decreasing and for all values of .

For the continuous function, there must be no breaks, holes or gaps in the graph.

For the decreasing function, the -value decreases as the -value increases.

For for all values of , the graph must be above the -axis. In other words the range of the function is all positive real numbers.

An exponential function is perfect model of a function for all values of .

Graph:

Observe the graph:

tends to go down as it goes along and for all values of .

Graph:

.