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13 February, 05:09

If the original cost of a TV is 1250.00 but decreases by 4.5% each week, how many weeks before the TV will cost 800.00?

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Answers (2)
  1. 13 February, 05:16
    0
    This is exponential growth/decay type problem ...

    F=Ir^t, F=final value, I=initial value, r=rate, t=time, in this case I=1250 and r = (1-.045) = 0.955 so

    F=1250 (.955) ^t and we want to find t for when F=800

    800=1250 (.955) ^t

    .64=.955^t take the natural log of both sides ...

    ln. 64=t ln. 955

    t = (ln. 64) / ln. 995

    t≈9.69 weeks

    t≈9.69 weeks (to nearest hundredth of a week)
  2. 13 February, 05:21
    0
    800=1250 (1-0.045) ^t

    Solve for t

    t=log (800:1,250) : log (1-0.045)

    t=9.7 weeks

    Check

    A=1,250 * (1-0.045) ^ (9.7)

    A=799.7=800
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