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