Question

The graph of f(t) = 6•2^t shows the value of a rare coin in year t. What is the
meaning of the y intercept?
Every year the coin is worth 6 more dollars.
B. In year 1, the coin was worth S12
C. When it was purchased (year 0), the coin was worth $2.
D. When it was purchased (year 0), the coin was worth $6

Answer 1

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.**