Juan purchased an antique that had a value of $200 at the time of purchase. Each year, the value of the antique is estimated to increase 10% over its value the previous year. The estimated value of the antique, in dollars, 2 years after purchase can be represented by the expression 200a, where a is a constant. What is the value of a?

Explanation

The correct answer is 1.21. It's given that each year, the value of the antique is estimated to increase by 10% over its value the previous year. Increasing a quantity by 10% is equivalent to the quantity increasing to 110% of its original value or multiplying the original quantity by 1.1. Therefore, 1 year after the purchase, the estimated value of the antique is 200(1.1) dollars. Then, 2 years after purchase, the estimated value of the antique is 200(1.1)(1.1), or 200(1.21) dollars. It's given that the estimated value of the antique after 2 years is 200a dollars. Therefore, 200(1.21) = 200a. It follows that a = 1.21.