Given:
The graph of [tex]f(t)=4 \cdot 2^t[/tex] shows the value of a rare coin in year t.
We need to determine the meaning of the y - intercept.
Meaning of the y - intercept:
Here, t represents the x - axis and f(t) represents the y - axis.
The value of y - intercept is the value of y when x = 0.
Hence, the the value of f(t) can be determined by substituting t = 0 in the function [tex]f(t)=4 \cdot 2^t[/tex]
Thus, we have;
[tex]f(0)=4 \cdot 2^0[/tex]
[tex]f(0)=4[/tex]
Thus, the value of the y - intercept is 4.
The y - intercept represents the value of the rare coin in year 0.
Therefore, the meaning of the y - intercept is "When it was purchased (year 0), the coin was worth $4".
Hence, Option B is the correct answer.
