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 $400,000. Two years ago, the value of the collection was $440,000 and last year, the collection was valued at $484,000. 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?

Accepted Solution

The rule you would use to represent the situation would be 400,000 + 40,000x. X would represent the number of years that have passed since the amount has been increasing at the same rate. You could use this expression to find her value of the art collection if you know how many years have passed since the constant rate began.