In the function \( f(t) = 6 \cdot 2^t \), the variable \( t \) represents the number of years since the initial time point (often taken to be year 0), and \( f(t) \) represents the value of the rare coin in year \( t \).
To find the y-intercept of the graph, we evaluate the function at \( t = 0 \):
\[ f(0) = 6 \cdot 2^0 = 6 \cdot 1 = 6 \]
The y-intercept of the graph is the point where the curve intersects the y-axis, which occurs when \( t = 0 \).
The meaning of the y-intercept, in this case, is that the value of the rare coin in year \( t = 0 \) (the starting point) is $6. This represents the initial value of the coin before any years have passed.