The function v (t) = 8 * (2.5) ^ t - 1 gives the value of a rare coin, in dollars, in year t. What does the value 8 particularly represent in the situation? (In the function, all of the equation t - 1 is an exponent, not just t.)

A. The coin was worth $8 in Year 1.

B. The coin increases in value b $8 each year.

C. In Year 1, a total of 8 coins were in circulation.

D. Each year, the coin is worth 8 times what it was worth the previous year.

I think it's A. But then again, when I think about it, I feel like it could be any of my answers.

Sometimes the easiest thing to do is test the hypotheses.

In order for A to be correct, when we plug 1 in for t, we should get 8.

2.5^ (1-1) = 2.5 ^ 0 = 1, so yes. In year one, the coin is valued at $8.

We have our answer, but for kicks let's do the rest.

For B, if we pick the year 2, the value should then be 16.

2.5 ^ (2-1) = 2.5 ^ 1 = 2.5. 8*2.5 = 20.

For C, there is no reason to infer number of coins. It has nothing to do with the question being answered.

For D, we look at the answers to A and B again. Is B 8 times A?

So, the only answer which comes back correct is A.