Chapter 4.1, Problem 67E

Efficiency of a machine operator. The rate at which a machine operator’s efficiency, E (expressed as a percentage), changes with respect to time t is given by

$\frac{dE}{dt}=30-10t$

Where t is the number of hour the operator has been at work.

A machine operator’s efficiency changes with respect to time.

Find $E\left(t\right)$, given that the operator’s efficiency after working 2 hr is that is, $E\left(2\right)=72$

Use the answer to part (a) to find the operator’s efficiency after 3 hr; after 5 hr.

With respect to time t is given by