the president announces that the national deficit is increasing but at a decreasing rate. Interpret this statement in terms of a function and its derivatives.
Please explain it to me in details... I have an exam coming up and I would like to understand this topic well.
2007-10-26 12:46:55 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The basic function is the deficit vs time. The first derivitive is always positive. However, the second derivitive is the rate of change of the 1st derivitive. It is decreasing, meaning that though the debt rises, it change/time is less than it used to be.
A good example is the "diminishing returns curve" y = A (1-exp(-kt))
Here, A is the max value of y at time -> infinite, and k is a parameter of the rate of increase of y. Its first derivitive is k exp(-kt)
and the second derivitive is - k^2 exp (-kt). Note that the first derivitive is always positive while the second derivitive is always negative.
2007-10-26 12:59:28 · answer #1 · answered by cattbarf 7 · 0⤊ 0⤋