Chapter 10.4, Problem 33E

Science Research in the United States The following table shows the number of science research articles authored by U.S researchers during the period 1980–2010:

$\begin{array}{l}\text{year }t\\ \left(\text{ year since 1980}\right)\end{array}$	0	5	10	15	20	25	30
$\begin{array}{l}\text{Articales }N\left(t\right)\\ \left(\text{thousands }\right)\end{array}$	170	200	220	260	252	290	340

a. Find the interval(s) over which the average rate of change of N was the greatest. What was that rate of change? Interpret your answer.

b. The percentage change of N over the interval $\left[a,b\right]$ is defined to be

Percentage change of $N=\frac{\text{ Change in }N}{\text{First value}}=\frac{N\left(b\right)-N\left(a\right)}{N\left(a\right)}$

Compute the percentage change of N over the interval $\left[0,30\right]$ and also the average rate of change. Interpret the answers.