Chapter 4.5, Problem 80E

Research and Development: Federal The total spent on research and development by the federal government in the United States during 2002–2012 can be approximated by

$S\left(t\right)=3.1\ln t+22\text{ billion dollars }\left(2\le t\le 12\right),$ where t is the year since 2000. What was the total spent in $2005\left(t=5\right)$, and how fast was it increasing? [HINT: See Quick Examples 1 and 2.]