Chapter 8.1, Problem 35E

To determine

Tofind the nearest whole number for the customers who arrives at the counter over the $60$ minute period.

Answer to Problem 35E

Approximately the value is found to be $725$ option (b).

Explanation of Solution

Given information:

The rate at which the customers arrive at a counter to be served is modelled by the function F defined by $F\left(t\right)=12+6\cos \left(\frac{t}{\pi }\right)$ for $0\le t\le 60$ where $F\left(t\right)$ is measured in customers per minute and $t$ is measured in minutes.

The number of customers arrive at the counter over the $60$ minute period is found by solving the integral,

  ${\displaystyle \underset{0}{\overset{60}{\int }}12+6\cos \left(\frac{t}{\pi }\right)}dt={\left[12t+6\pi \sin \left(\frac{t}{\pi }\right)\right]}_0^{60}\approx 725$

Therefore, approximately the value is found to be $725$ option (b).