Our function is f(t) = e^t−a. This is an exponential function (see Graphs of Exponential Functions).

When t = a, the graph has value e^a−a = e⁰ = 1.

The function has the form:

We will use the Time Displacement Theorem:

Now, in this example,

[NOTE: e^b−a is a constant, which we introduce for convenience.]

[Each part is now in the form u(t − a)g(t − a), so we can apply the Time Displacement Theorem.]