Question

As part of a quality-control program, the chess sets manufactured by Jones Brothers are subjected to a final inspection before packing. The rate of increase in the number of sets checked per hour by an inspector t hr into the 8 a.m. to 12 noon shift is approximately:

N'(t) = −3t^2 + 12t + 45 (0 <_ t <_4).
(a) Find an expression N(t) that approximates the number of sets inspected at the end of t hours.

Answer 1

Answer:
`N(t)=-t^3+6t^2+45t`

Explanation:

Since we have given that

`N'(t)=-3t^2+12t+45`

in between (0≤t≤4).

We need to find N(t) that approximates the number of sets inspected at the end of t hours.

So, it becomes,

`N(t)=\int\limits^4_0 {N'(t)} \, dt\\\\N(t)=\int\limits^4_0 {-3t^2+12t+45} \, dt\\\\N(t)=(-3t^3)/(3)+12(t^2)/(2)+45t|^4_0\\\\N(t)=-(4)^3+6(4)^2+45(2)\\\\N(t)=122`

Hence,
`N(t)=-t^3+6t^2+45t`