Example 2 (2004 College Entrance Examination Hunan Paper) Farmers' income consists of wage income and other income. In 2003, the per capita income of farmers in a certain area was 3150 yuan (of which wage income was 1800 yuan, and other income was 1350 yuan). It is expected that in the 5 years from 2004, farmers' wage income will grow at an annual growth rate of $6 \%$, and other income will increase by 160 yuan each year. Based on the above data, the per capita income of farmers in the region in 2008 will be between ( ).
A. 4200 yuan $\sim$ 4400 yuan
B. 4400 yuan $\sim$ 4600 yuan
C. 4600 yuan $\sim$ 4800 yuan
D. 4800 yuan $\sim$ 5000 yuan
Choose B. Reason: According to the problem, the per capita income of farmers in the region in 2008 is $1800 \times(1+6 \%)^{5}+1350+5 \times 160$, and an approximate calculation is made for the expansion of $(1+6 \%)^{5}$.
$$
\begin{array}{l}
1800 \times(1+6 \%)^{5}+1350+5 \times 160>1800 \times\left(1+5 \times 0.06+10 \times 0.06^{2}\right)+1350+800=4554.8, \\
1800 \times(1+6 \%)^{5}+1350+5 \times 160<1800 \times\left(1+5 \times 0.06+10 \times 0.06^{2}+0.03\right)+2150=4560.2 .
\end{array}
$$

Therefore, the per capita income of farmers in the region in 2008 is between 4400 yuan and 4600 yuan.