IV. From 1981 to the end of this century, a total of twenty years, our country's industrial and agricultural total output value needs to quadruple, so what is the approximate average annual growth rate?
iv. Solution Let the average annual growth rate be $x$, then according to the problem,
$$
(1+x)^{20}=4 \text{. }
$$

Taking the logarithm with base 10 on both sides,
$$
\begin{array}{l}
20 \lg (1 \div x)=2 \lg 2 . \\
\lg (1+x)=\frac{1}{10} \lg 2=0.0301 . \\
1+x \approx 1.072 . \\
\therefore x \approx 0.072=7.2\% .
\end{array} .
$$

Answer: The average annual growth rate is $7.2\%$.