Question

What is the initial value for the function f(x)=3(5/4)x

Answer 1

For
$f(x)=3\left(\dfrac{5}{4}\right)^{x}$
you seem to want to know the value of f(0). Put 0 where x is, then evaluate.
$f(0)=3\left(\dfrac{5}{4}\right)^{0}=3\cdot 1=3$

The initial value of the function is 3.

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You will observe that when x=0, the exponential term evaluates to 1. This is true regardless of its base. Thus f(0) is always the coefficient of the exponential term—in this case, 3.

Answer 2

If you meant for f(x)=3(5/4)x to represent an exponential function, please use " ^ " to indicate exponentiation:

f(x)=3(5/4)^x

The initial value is the value of f(x) when x = 0:  f(0) = 3(5/4)^0 = 3(1) = 3.