Step-by-step explanation:
We have a function in the form
[tex]f(x)=a(b^x)[/tex]
The initial value of a function refers to the value of the function when x=0.
If we plug in x=0 into our function, we get
[tex]f(x)=a(b^x)\\\\f(0)=a(b^0)[/tex]
Any number to the power of 0 is equal to 1, so we can rewrite this function as
[tex]f(0)=a(1)\\\\f(0)=a[/tex]
Here we can see that we have just shown why the initial value of any function in the the given form is equal to a.
