The following table gives the national income and the population of a country for the years 1984 – 85 to 1989 – 90. For each o the following questions choose the best alternative:

1985-86: \( \frac{75.0 - 74.0}{74.0} \times 100 \approx 1.35\% \)
1986-87: \( \frac{77.0 - 75.0}{75.0} \times 100 \approx 2.67\% \)
1987-88: \( \frac{78.5 - 77.0}{77.0} \times 100 \approx 1.95\% \)
1988-89: \( \frac{80.0 - 78.5}{78.5} \times 100 \approx 1.91\% \)
1989-90: \( \frac{81.5 - 80.0}{80.0} \times 100 \approx 1.88\% \)
1985-86: \( 12.41 - 1.35 \approx 11.06\% \)
1986-87: \( 8.73 - 2.67 \approx 6.06\% \)
1987-88: \( 10.98 - 1.95 \approx 9.03\% \)
1988-89: \( 15.57 - 1.91 \approx 13.66\% \)
1989-90: \( 9.65 - 1.88 \approx 7.77\% \)
\( = 13.66\% \text{ in } 1988-89 \)





For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: