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Math Help - Rational Inequalities

  1. #1
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    Rational Inequalities

    A biologist predicted that the population of tadpoles in a pond could be modelled by the function f(t)= (40t)/((t^2)+1), where t is given in days. The function that actually models the tadpole population is g(t) = (45t) / ((t^2)+8t + 7).
    Determine where g(t) > f(t).

    There are a string of these problems.. How would I solve these kinds of questions?
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  2. #2
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    Quote Originally Posted by willman32 View Post
    Determine where g(t) > f(t).
    I'll get you started

     \frac{45t}{t^2+8t + 7} > \frac{40t}{t^2+1}

    Divide both sides by 5t

     \frac{9}{t^2+8t + 7} > \frac{8}{t^2+1}

    then cross multipling

     9(t^2+1) >8(t^2+8t + 7)

    expanding

     9t^2+9 >8t^2+64t + 56

    and grouping all terms to 1 side

     t^2-64t-47 >0

    now you just need to solve this quadratic.
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