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.

Show all Work! 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.

 Apr 15, 2021

Common  ratio  is    810000.450000  = 9/5  =  1.8


A)  Explicit  rule  is


Value  at the  end of   year  n    =   450000 (1.8)^n



B)  After 12  years  the  value  is


450000(1.8)^12   ≈   $ 520, 574,122



cool cool cool

 Apr 15, 2021

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