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# An antique silk rug is worth $12000 after it has appreciated by 5 % for ten consecutive years. How much was it worth ten years ago? 0 33 2 An antique silk rug is worth$12000 after it has appreciated by 5 % for ten consecutive years. How much was it worth ten years ago?

i dont understand what "appreciated by 5%" means. can anyone help?

Aug 21, 2023
edited by Guest  Aug 21, 2023

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First, the word 'appreciated' means increased in value. If a house appreciates in value by 20%, it is now worth 20% more than its original price.

Let us call the original value of the rug $$x$$. We know that the rug is worth 105% of what it was worth 10 years ago. We can write this as

$$12000 = 105\% \cdot x$$. Converting the percent to a decimal gives us the equation $$12000=1.05x$$. Dividing both sides by 1.05 gives us our final answer: $$x \approx \11428.57$$. (Rounded to the nearest cent.) So, the antique rug was worth approximately $11428.57. Aug 21, 2023 #2 0 Let the price of rug 10 years ago ==P "Appreciate" - means it goes up in value by 5% per year P ==12,000 / 1.05^10 P ==12,000 / 1.628895 P ==$7,366.96 - price of the rug 10 years ago

Aug 21, 2023