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Math Help - Please Help: Rational functions problem

  1. #1
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    Please Help: Rational functions problem

    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).
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    Quote Originally Posted by BuffaloSoulja View Post
    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).
    you need to solve \frac {45t}{t^2 + 8t + 7} > \frac {40t}{t^2 + 1}

    Bring everything to the left side, combine, simplify and set both the numerator and denominator equal to zero. Solve for the t-values. Plot those on a number line, and test the intervals to see which ones you need.

    can you finish?
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  3. #3
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    Quote Originally Posted by BuffaloSoulja View Post
    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).
    g(t)>f(t)

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

    45t(t^2+1) > 40t(t^2+8t+7)

    45t^3+45t > 40t^3+320t^2+280t

    5t^3-320t^2-235t > 0

    Can you solve it from here?
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  4. #4
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    Quote Originally Posted by pickslides View Post
    g(t)>f(t)

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

    45t(t^2+1) > 40t(t^2+8t+7)

    45t^3+45t > 40t^3+320t^2+280t

    5t^3-320t^2-235t > 0

    Can you solve it from here?

    Alright. I got to 5t(t^2-64t-47)/(t+1)(t+7)(t^2+1) >0

    I can just cancel out the denominator? Would I not lose solutions?
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  5. #5
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    Quote Originally Posted by BuffaloSoulja View Post
    Alright. I got to 5t(t^2-64t-47)/(t+1)(t+7)(t^2+1) >0

    I can just cancel out the denominator? Would I not lose solutions?
    I get

    5t(t^2-64t-47) >0

    not sure how you found those terms in the denominator.

    Now just factor the quadratic.
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  6. #6
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    Quote Originally Posted by pickslides View Post
    I get

    5t(t^2-64t-47) >0

    not sure how you found those terms in the denominator.

    Now just factor the quadratic.

    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) * (t^2+1)/(t^2+1)-40t/(t^2+1) * (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

    This is what i did btw
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