Questions: 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? A. When it was purchased (year 0), the coin was worth 6. B. When it was purchased (year 0), the coin was worth 2. C. Every year the coin is worth 6 more dollars. D. In year 1, the coin was worth 12.

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?
A. When it was purchased (year 0), the coin was worth 6.
B. When it was purchased (year 0), the coin was worth 2.
C. Every year the coin is worth 6 more dollars.
D. In year 1, the coin was worth 12.

Transcript text: The graph of $f(t)=6 \cdot 2^{t}$ shows the value of a rare coin in year $t$. What is the meaning of the $y$-intercept? A. When it was purchased (year 0 ), the coin was worth $\$ 6$. B. When it was purchased (year 0 ), the coin was worth $\$ 2$. C. Every year the coin is worth 6 more dollars. D. In year 1, the coin was worth $\$ 12$.

Solution

Solution Steps

Step 1: Analyze the y-intercept

The y-intercept is the point where the graph intersects the y-axis. This occurs when $t = 0$. In this context, $t=0$ represents the initial year or when the coin was purchased.

Step 2: Evaluate the function at t=0

Substitute $t=0$ into the function $f(t) = 6 \cdot 2^t$. $f(0) = 6 \cdot 2^0 = 6 \cdot 1 = 6$

Step 3: Interpret the result

The y-intercept is at $(0, 6)$. This means that when $t=0$ (the year of purchase), the value of the coin, $f(t)$, is $6.