Let N N0ekt. In this exercise we show that if t is very
Chapter 5, Problem 63(choose chapter or problem)
Let N N0ekt. In this exercise we show that if t is very small, then N/t kN. In other words, over very small intervals of time, the average rate of change of N is proportional to N itself. (a) Show that the average rate of change of the function N N0ekt on the interval [t, t t] is given by (b) In Exercise 26 of Section 5.2 we saw that e x x 1 when x is close to zero. Thus, if t is sufficiently small, we have ekt k t 1. Use this approximation and the result in part (a) to show that N/t kN when t is sufficiently close to zero. N
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