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 $\$ 12$.
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Solution

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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=0t = 0. In this context, t=0t=0 represents the initial year or when the coin was purchased.

Step 2: Evaluate the function at t=0

Substitute t=0t=0 into the function f(t)=62tf(t) = 6 \cdot 2^t. f(0)=620=61=6f(0) = 6 \cdot 2^0 = 6 \cdot 1 = 6

Step 3: Interpret the result

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

Final Answer A. When it was purchased (year 0), the coin was worth $6.

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