To find the y-intercept of the function modeled by the equation
\[ A(t) = 3,000(1.14)^t, \]
we need to evaluate the function at \( t = 0 \).
Substituting \( t = 0 \) into the equation:
\[ A(0) = 3,000(1.14)^0. \]
Since any number raised to the power of 0 equals 1:
\[ A(0) = 3,000 \cdot 1 = 3,000. \]
Thus, the y-intercept of the equation is \( 3,000 \).
Therefore, the answer is:
\[ \boxed{3000}. \]