The population in a certain city was 55,000 in 2000 , and its future size is predicted to be $P(t)=55,000 e^{0.017}$, where $t$ is the number of years after 2000 . Complete parts a through d below. a. Does this model indicate that the population is increasing or decreasing? decreasing increasing b. Use this function to estimate the population of the city in 2003. (Round to the nearest whole number as needed.)

Step 1 ：The population in a certain city was 55,000 in 2000, and its future size is predicted to be \(P(t)=55,000 e^{0.017t}\), where \(t\) is the number of years after 2000.

Step 2 ：a. This model indicates that the population is \(\textbf{increasing}\).

Step 3 ：b. To estimate the population of the city in 2003, we need to find the value of \(P(t)\) when \(t=3\) (since 2003 is 3 years after 2000).

Step 4 ：Substitute \(t=3\) into the function \(P(t)=55,000 e^{0.017t}\).

Step 5 ：Calculate the result to get \(P_t = 57877.75913057621\).

Step 6 ：Round \(P_t\) to the nearest whole number to get \(57878\).

Step 7 ：Final Answer: The estimated population of the city in 2003 is \(\boxed{57878}\).