To represent the value of the collection after 3 years if it appreciates at a rate of 3% per year, we can use the following equation:
V = P(1 + r)^t
Where:
V = the value of the collection after 3 years
P = the initial value of the collection, which is $390 in this case
r = the annual appreciation rate, which is 3% or 0.03 as a decimal
t = the number of years, which is 3 in this case
Substituting the given values, we get:
V = $390(1 + 0.03)^3
Simplifying the equation, we get:
V = $390(1.03)^3
V = $390(1.0927)
V = $426.99 (rounded to the nearest cent)
Therefore, the equation that represents the value of the collection after 3 years if it appreciates at a rate of 3% per year is:
V = $390(1.03)^3
V = $426.99