A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is given by the function `l(t) = t^2 - sqrt(t)`, and the change in width is given by `w(t) = t^2 - 2t^(1/2)`. Which function gives the change in area of the metal strip`
a.a(t) = t^4 + 2t

b.a(t) = t^4 + 2t + 3t^(5/2)

c.a(t) = t^4 - 3t^(5/2) + 2t`

d.a(t) = t^4 + 2t - 2t^(1/2) + sqrt(t)

Question

A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is given by the function `l(t) = t^2 - sqrt(t)`, and the change in width is given by `w(t) = t^2 - 2t^(1/2)`. Which function gives the change in area of the metal strip`
a.a(t) = t^4 + 2t

b.a(t) = t^4 + 2t + 3t^(5/2)

c.a(t) = t^4 - 3t^(5/2) + 2t`

d.a(t) = t^4 + 2t - 2t^(1/2) + sqrt(t)