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Thread: Natural growth question

  1. #1
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    Natural growth question

    The cost C of an article is rising with inflation in such a way that at the start of every month, the cost is 1% more than it was a month before. Let C0 be the cost at time zero.

    a) I figured out that C= C0 x1.01^t. The question is find the percentage increase in the cost over 12 months.

    b) I figured out that C=C0e^kt and k=ln1.01 given t=1, C=1.01C0. But how do you find the
    I) percentage increase in the cost over twelve months?
    II) the time required for the cost to double?

  2. #2
    617 pages fan96's Avatar
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    Re: Natural growth question

    Unless the question specifically asks for it, it's not necessary to use here.

    Let the initial cost be , or . We don't actually need to know what the initial cost is, we're only interested in its percentage change.

    Then, the cost after months is given, as a percentage of the initial cost, by .

    will give the cost after 12 months as a percentage of the original. Subtract from it to get the increase in percentage cost.

    The time required for the cost to double can be found by setting and solving for .
    Last edited by fan96; 23 Apr 2018 at 12:00 AM.
    HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]

    1(3√3) t2 dt cos(3π/9) = log(3√e) | Integral t2 dt, From 1 to the cube root of 3. Times the cosine, of three pi over nine, Equals log of the cube root of e.

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