Answer
(a) $270.08$
(b) See figure, increases $(0,5.9)\cup(9.5,15)$, decreases $(5.9,9.5)$
Work Step by Step
Given $f(t)= 1.06t^3 - 24.6t^2 + 180t$, we have:
(a) for $t=2$, $ƒ(2)= 1.06(2)^3 - 24.6(2)^2 + 180(2)=270.08$
(b) Graph the function as shown in the figure, we can find that the function increases over $(0,5.9)\cup(9.5,15)$ and decreases over $(5.9,9.5)$