Madame Dumas has a rather extensive art collection and the overall value of her collection has been increasing each year. Three years ago, her collection was worth $450,000. Two years ago, the value of the
collection was $810,000 and last year, the collection was valued at $1,458,000.
Assume that the rate at which Madame Dumas's art collection's value increase remains the same as it has
been for the last three years. The value of the art collection can be represented by a geometric sequence.
The value of the collection three years ago is considered the first term in the sequence.
A) Write an explicit rule which can be used to determine the value of her art collection n years after that.
B) Use this rule to determine the value of her collection 12 years after she started tracking its worth
rounded to the nearest dollar.