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Help in need! : Rational functions problem

  1. Mar 14, 2010 #1
    1. The problem statement, all variables and given/known data
    A scientist predicted that the population of fish in a lake could be modeled by the function f(t)= 40t/(t^2+1), where t is given in days. The function that actually models the fish population is g(t)=45t/(t^2+8t+7). Determine where g(t)>f(t).


    2. Relevant equations

    f(t)= 40t/(t^2+1)
    g(t)=45t/(t^2+8t+7)
    g(t)>f(t)

    3. The attempt at a solution

    g(t)>f(t)
    45t/(t^2+8t+7)>40t/(t^2+1)
    45t/(t+1)(t+7)-40t/(t^2+1)>0
    Find LCD by multiplying 1
    45t/(t+1)(t+7) x (t^2+1)/(t^2+1)-40t/(t^2+1) x (t+7)(t+1)/(t+7)(t+1) > 0
    Simplifies to
    (5t^3-320t^2-235t)/(t+1)(t+7)(t^2+1)
    5t(t^2-64t-47)/(t+1)(t+7)(t^2+1) >0

    Am i doing this correct? I don't know what to do next.
     
  2. jcsd
  3. Mar 14, 2010 #2

    PAR

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    Another way of doing it is to find where f(t) and g(t) intersect and then evaluate the equations at values a little bit off those intersection points to find which one is higher

    So i suggest you solve:

    [tex]\frac{40t}{(t^2+1)}[/tex] = [tex]\frac{45t}{(t^2+8t+7)}[/tex]

    Step one should be multiplying both sides by [tex](t^2+8t+7)[/tex] and [tex](t^2+1)[/tex]
     
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