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Computer Sales

  1. Sep 25, 2016 #1
    1. The problem statement, all variables and given/known data
    Between 1985 and 1995 the number of computers in thousands sold in canada is estimated by c(t) = 0.92(t^3 + 8t^2 + 40t +400)
    In what year did home computers sale reach 1.5 million?
    2. Relevant equations


    3. The attempt at a solution
    I know I have to isolate the t to obtain time. So far this is what I have gotten up to

    1230.43 = t^3 + 8^2 + 40t
    Here is where I am stuck. Would I have to factor out a t in order to move on to th next step?
     
  2. jcsd
  3. Sep 25, 2016 #2

    Math_QED

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    There are formulas to find the roots of any third degree polynomial. However, I assume that you did not cover those formulas in class. In exercises where you are not allowed to use a calculator, you can 'guess' one of the roots and then use something like synthetic division to find the remaining quadratic polynomial. In this case however, this seems quite impossible so I would use a calculator. Note too that you wrote 8^2 instead of 8t^2.
     
  4. Sep 25, 2016 #3

    Mark44

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    The second term on the right should be 8t2. I'm assuming, but didn't verify, that the 1230.43 number has the 400 term already folded in.

    Although there is a technique for solving third-degree polynomials, it's not something I have committed to memory, and it's very complicated. One approach would be to graph the equation C = t3 + 8t2 + 40t, and find the point at which the C value is at or close to 1230.43, then read off the t value at that point.

    Another approach is to start with an education guess, say t = 10, and see what C value you get, adjusting t up or down in successive calculations.
     
  5. Sep 25, 2016 #4

    SammyS

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    Factoring is only useful for the case where the othe side of the equation is zero.

    By the way, what is the definition of the variable, t ?
     
  6. Sep 25, 2016 #5
    Sorry about that I meant 8t^2. The book uses a graphing calculator however we were meant to solve it algebraically:/
     
  7. Sep 25, 2016 #6
    T is for time.
     
  8. Sep 25, 2016 #7

    Ray Vickson

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    The exact solution is very complicated to get. Typically in such a problem, we unashamedly employ numerical methods, such as graphical analysis, resorting to a spreadsheet or computer algebra system, or using a decent scientific calculator.

    For an exact method, see, eg.,
    http://www.math.vanderbilt.edu/~schectex/courses/cubic/
     
    Last edited: Sep 25, 2016
  9. Sep 25, 2016 #8

    SammyS

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    Yes, time. But how is that time measured?
    For the year 1985 is t = 1985 ?
     
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