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?

Answer 1

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