Final answer:
The value of the rare coin can be represented by an exponential growth function, V(t) = 625(1 + 0.045)^t, where V(t) is the value of the coin after t years, and the coin appreciates at 4.5% per year.
Step-by-step explanation:
To represent the situation where the value of a rare coin is appreciating at a certain rate, we can use an exponential growth function. Given that the starting value of the coin is $625 and it appreciates at a rate of 4.5% per year, the function can be written as:
V(t) = P(1 + r)^t
where:
- V(t) is the value of the coin after t years,
- P is the principal amount (initial value of the coin), which is $625,
- r is the annual appreciation rate, which is 4.5% or 0.045 as a decimal,
- t is the time in years.
Therefore, the function would be:
V(t) = 625(1 + 0.045)^t