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 $500,000. Two years ago, the value of the collection was $550,000 and last year, the collection was valued at $605,000.

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.

Write an explicit rule which can be used to determine the value of her art collection n years after that. Use this to determine the value of her collection 10 years after she started tracking its worth rounded to the nearest dollar.

Show work, please.

VanillaVi Apr 5, 2020

#1**+1 **

500 000 to 550 000 is 10% increase or geometric ratio 1.1

future value would be 500 000 (1.1)^{n }where n = years

ElectricPavlov Apr 5, 2020

#2**0 **

If you start the sequence, you will see that each term is 10% greater than the term before.

So 10 years later would be 500,000*\(1.1^{10}\) which is $1296871.23 or just $1,296,871

MooMooooMooM Apr 5, 2020