Question

Worker Efficiency An efficiency study conducted for Elektra Electronics showed that the number of Space Commander walkie-talkies assembled by the average worker during the morning shift t hr after starting work at 8 a.m. is given by

N(t) = −t3 + 6t2 + 15t (0 ≤ t ≤ 4).

(a) Find the rate at which the average worker will be assembling walkie-talkies t hr after starting work.
(b) At what rate will the average worker be assembling walkie-talkies, per hour, at 9 a.m.?walkie-talkies/hour At what rate will the average worker be assembling walkie-talkies, per hour, at 10 a.m.?
(c) How many walkie-talkies will the average worker assemble between 9 a.m. and 10 a.m.?walkie-talkies

Answer 1

a) -2t²+12t+15 b) 25, 31 c) 26

Explanation:

a) To find out rate, we will take derivative of the given equation

dN/dt= -2t2+12t+15

b) At 9 am , it will be 1hr since the start of morning shift so t=1

dN/dt= -2(1)²+12(1)+15

dN/dt=25

At 10 am, it will 2 hrs since the start of morining shift be so t=2

dN/dt=-2(2)²+12(2)+15

DN/dt= 31

c) N(2)-N(1)= (-(2)³+6(2)²+15(2))-(-(1)³+6(1)²+15(1))

=(46)-(20))

= 26