The profit function for the manufacture of a given item expresses the profit P in terms of...

The profit function for the manufacture of a given item expresses the profit P in terms of the number x of items manufactured. The profit function for a certain item has been determined to be

where both x and P are in thousands. The equation

was used to approximate the profit function for the range 0 ≤ x ≤ 100. For what values of x does the approximation give the exact value of the profit? What happens if we try to extend the approximation beyond x = 100? [Hint: Graph these two equations.]