2. Functions from Verbal Statements

Example 1

When operating a factory, there are fixed costs like electricity, labor and storage space. One such factory has fixed costs of `$50,000` per day.

There are also variable costs, for example, if they make more widgets it will cost more in materials, extra labor costs and extra power costs. The factory calculates there is a variable cost of `$10` to manufacture each extra widget.

Write the daily cost C as a function of the number of units produced.

Example 2

norman window

A Norman window has the shape of a rectangle with a semicircle on top, as shown.

Considering the space available, the base of each window has to be `30\ "cm"` less than the height of the rectangular part.

What is the perimeter p of the window as a function of the radius r of the circular part?

Exercise

A Boeing 747 burns fuel at the rate of `13,000\ "kg/h"` while cruising. If the aircraft weighed `350,000\ "kg"` at take-off, express its weight w as a function of the time t, in hours.