Answer to Question #143734 in Calculus for Kate

Question

In deciding how long a resident’s shift in the emergency room should be, the Chief of Staff at Vancouver General Hospital would like to minimize the average rate at which errors are made. Let E(t) be the number of errors made by a resident from the start of a shift until t hours into the shift. The instantaneous rate of change of errors made is E′(t) = t3 − 3 t2 + 2. Explain, as you would to a hospital administrator, why it makes sense to minimize A(t) rather than E(t).

Answer 1

We should minimize average rate of erors A(t)=

$$\int E'(t)$$

because it represents total number of erors, that makes resident from the start of a shift until t hours into the shift. E(t) represent the number of erors at the moment. In next time it will be another. So E(t) don't represent the total number of erors during some time.