The profit of football club after a take over is modelled by p(t)=t3-24t2+20t+120 in which years was the club making losd?

Question

The profit of football club after a take over is modelled by p(t)=t3-24t2+20t+120 in which years was the club making losd?

in progress 0
RobertKer 4 years 2021-08-01T04:28:41+00:00 1 Answers 18 views 0

Answers ( )

    0
    2021-08-01T04:29:59+00:00

    Answer:

    16 years

    Step-by-step explanation:

    Given

    P(t) = t^3 - 24t^2 + 20t + 120

    Required

    Year they made loss

    P(t) = t^3 - 24t^2 + 20t + 120

    Start by differentiating P w.r.t t

    Using first principle:

    \frac{dP}{dt} = 3t^2 - 48t + 20

    Equate to 0, in order to solve for t

    \frac{dP}{dt} = 0

    So, we have:

    3t^2 - 48t + 20 = 0


    Solve using quadratic equation

    t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}

    Where

    a = 3, b = -48 and c = 20

    So, we have:

    t = \frac{-(-48) \± \sqrt{(-48)^2 - 4*3*20}}{2*3}

    t = \frac{-(-48) \± \sqrt{2064}}{2*3}

    t = \frac{-(-48) \± \45.4}{2*3}

    t = \frac{48 \± \45.4}{6}

    Split:

    t = \frac{48 + \45.4}{6} or t = \frac{48 - \45.4}{6}

    t = \frac{93.4}{6} or t = \frac{2.6}{6}

    t = 15.56 or t = 0.43

    Approximate to whole numbers

    t = 16 or t = 0

    Hence, they made loss 16 years after they took over

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )