Recall that to find the cost to produce the $n$th unit in a production process, we calculate the difference
$$C(n) - C(n-1)$$ where $C(n)$ is the cost of producing $n$ units.

The total cost (in dollars) for a fast food franchise of producing $x$ thousand hamburgers might be

$$C(x) = 13000 + 800 x - 20 x^2.$$

Find the exact cost of producing the 2,001st burger. Be careful though. The units for $x$ are thousand of hamburgers. The 2,001st burger is represented by 2.001!

Exact cost of 2,001st burger = $

Use marginal cost to approximate the cost of producing the 2001st burger.

Approx. cost of 2001st burger = $