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Algebra I

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The historical society tells him that furniture similar to his has been appreciating in value at 10% per year for the last 20 years and that his furniture could be worth $10,000 now.

Is my expression 10,000(1+.1)^x?
If so, I have to find what it costed 20 years ago. Would I just raise the expression to the power of 20, or -20?

  • Algebra I -

    no

    let the amount that it "costed" 20 years ago be x
    then x(1.1)^20 = 10000
    x = 10000/(1.1^20)

    I get 1486.44

    you might have seen the formula
    Present Value = amount (1+i)^-n
    then Present value = 10000(1.1)^-20
    = 1486.44

    If you know about negative exponents you will realize that the two equations are the same.

  • Algebra I -

    A new machine was purchased at the beginning of one year for $200. Each year the machine loses value. It is worth 90% as much as the previous year. What is the value of the machine at the end of the 4th year.

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