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

16 years

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:

`(dP)/(dt) = 3t^2 - 48t + 20`

Equate to 0, in order to solve for t

`(dP)/(dt) = 0`

So, we have:

`3t^2 - 48t + 20 = 0`

Solve using quadratic equation

`t = (-b \± √(b^2 - 4ac))/(2a)`

Where

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

So, we have:

`t = (-(-48) \± √((-48)^2 - 4*3*20))/(2*3)`

`t = (-(-48) \± √(2064))/(2*3)`

`t = (-(-48) \± \45.4)/(2*3)`

`t = (48 \± \45.4)/(6)`

Split:

`t = (48 + \45.4)/(6)` or
`t = (48 - \45.4)/(6)`

`t = (93.4)/(6)` or
`t = (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