Chapter 3.4, Problem 34E

Science Research in Europe The following table shows the number of science research articles authored by researchers in the European Union 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
$\begin{array}{l}\text{Articales }N\left(t\right)\\ \left(\text{thousands }\right)\end{array}$	140	170	190	260	300	340	430

a. Find the interval(s) over which the average rate of change of N was the least positive. 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 $\left[10,30\right]$ and also the average rate of change. Interpret the answers.