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Math Help - Geometric Series 2

  1. #1
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    Geometric Series 2

    An advertising company designs a campaign to introduce a new product to the city. The company determines that 1000 people are aware of the product at the beginning of the campaign. The number of new people aware increases 40% ever 10 days. What is the total number of people who are aware after 100 days?

    My attempt:

    t1 = 1000 r = 0.40 per 10 days n = 100

    0.40 / 10 = .04 per day

    r = .04

    Sn = t1r^n - 1 / r - 1

    S100 = (1000)(.04^100) - 1 / .04 - 1

    S100 = .96153...

    The correct answer is 98,739, I am WAY off. Can someone please help me, I am really confused...
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  2. #2
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    Re: Geometric Series 2

    Since you end up with 40% MORE every ten days, the common ratio is actually 1.4, not 0.4. Also, since your unit of time is "every 10 days", for 100 days, that means n is 10, since 10x10 = 100.
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  3. #3
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    Re: Geometric Series 2

    My attempt:

    t1 = 1000 r = 1.4 per 10 days n = 10

    Sn = t1r^n - 1 / r - 1

    S10 = (1000)(1.4^10) - 1 / 1.4 - 1

    S10 = 72,311

    The correct answer is 98,739, I'm still getting it wrong, but atleast it was closer this time...
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