To find the meaning of the y-intercept in the context of the function \( f(t) = 6 \cdot 2^t \), we need to evaluate the function at \( t = 0 \), as the y-intercept occurs when \( t = 0 \).
Calculating \( f(0) \):
\[ f(0) = 6 \cdot 2^0 = 6 \cdot 1 = 6 \]
This means that when \( t = 0 \) (the year when the coin was purchased), the value of the coin is $6.
Thus, the correct interpretation of the y-intercept is:
D. When it was purchased (year 0), the coin was worth $6.