Chapter 13.2, Problem 92E

Scientific Research: 1983–2003 The number of research articles in the prominent journal Physical Review written by researchers in the United States during 1983–2003 can be approximated by

$U\left(t\right)=\frac{4.6e^{0.6t}}{0.4+e^{0.6t}}$ thousand articles per year, $\left(0\le t\le 20\right)$, where t is time in years. ( $t=0$ represents 1983.)¹⁸

a. Find an (approximate) expression for the total number of articles written by researchers in the United States since 1983 $\left(t=0\right)$

[HinT: See Example 5.]

b. Roughly how many articles were written by researchers in the United States from 1983 to 2003?