Question

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, percent 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 ?

Answer 1

Answer: a= 1.21

Step-by-step explanation:

Note: This is a compound interest problem

Step 1

The value of the antique after one year is:

100% + 10% of the purchase price

= 110% of 200

=110/100 of 200

=1.10 × 200

Step 2

The value after two years is:

110% of the value after one year

=110% of (1.10 × 200)

=110/100 of (1.10× 200)

=1.10×(1.10×200)

=1.21×200

Step 3

Expressing the above solutionin the form 200a:

= 200× a = 200 × 1.21

|a=1.21

Thanks