Question 292578
Laboratories it was found that the number of components
assembled per hour by the average worker t hours after
starting work could be modeled by the formula
N(t)=-3t^3+23t^2+8t.
a) Rewrite the formula by factoring the right-hand side
completely.
N(t)=-3t^3+23t^2+8t
N(t)=t(-3t^2+23t+8)
N(t)=t(-3t^2+24t-t+8)
N(t)=t((-3t^2+24t)-(t-8))
N(t)=t(3t(-t+8)-(t-8))
N(t)=t(-3t(t-8)-(t-8))
N(t)=t(t-8)(-3t-1)
.
b) Use the factored version of the formula to find N(3)
N(t)=t(t-8)(-3t-1)
N(3)=3(3-8)(-3(3)-1)
N(3)=3(-5)(-9-1)
N(3)=3(-5)(-10)
N(3)=(-15)(-10)
N(3)=150