Madame Pickney 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 $600,000. Two years ago, the value of the collection was $690,000 and last year, the collection was valued at $793,500. Assume that the rate at which Madame Pickney'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. What explicit rule can be used to determine the value of her art collection n years after that? an=600,000 (1.15) n-1 an=600,000 (1.1) n+1 an=600,000 (1.9) n-1 an=600,000 (0.1) n-1

Question

Mathematics

Cristian Neal

2 March, 00:25

Madame Pickney 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 $600,000. Two years ago, the value of the collection was $690,000 and last year, the collection was valued at $793,500. Assume that the rate at which Madame Pickney'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. What explicit rule can be used to determine the value of her art collection n years after that? an=600,000 (1.15) n-1 an=600,000 (1.1) n+1 an=600,000 (1.9) n-1 an=600,000 (0.1) n-1

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Neveah Lawson · Answer 1

Given:

Three years ago, her collection was worth $600,000.

Two years ago, the value of the collection was $690,000

last year, the collection was valued at $793,500.

The explicit rule that can be used to determine the value of her art collection n years after that is:

an=600,000 (1.15) ^n-1

To check:

a (1) = 600,000 (1.15) ^1-1 = 600,000 (1.15 ⁰) = 600,000 (1) = 600,000

a (2) = 600,000 (1.15) ^2-1 = 600,000 (1.15¹) = 600,000 (1.15) = 690.000

a (3) = 600,000 (1.15) ^3-1 = 600,000 (1.15²) = 600,000 (1.3225) = 793,500