5. The population of a small mining town was 13700 in the year 2000 . Each year, the population decreases by an average of $5 \%$. a) What is the exponential equation that models this situation? b) Use your equation to find the population of the town in the year 2010.

Step 1 ：Given the initial population P0 = 13700, the decrease rate r = 0.05, and the time t = 10 years, we can use the exponential equation P(t) = P0 * (1 - r)^t to model the situation.

Step 2 ：Plugging in the values, we get P(10) = 13700 * (1 - 0.05)^10. Calculating this, we find the population in 2010 to be approximately \(\boxed{8203}\).