Answer :
The model for the city’s population is given by
$$
P = 250000 \cdot (1.03)^z,
$$
where $z$ represents the number of years after the year 2000.
1. Notice that the factor $1.03$ is raised to the power $z$, which means that for each additional year the population is multiplied by $1.03$.
2. Since $1.03$ can be written as $1 + 0.03$, this indicates that the population increases by $0.03$ times (or $3\%$) of its previous value each year.
3. Therefore, the statement "The population is increasing by $3\%$ each year" correctly interprets the factor $1.03$ in the model.
Thus, the correct answer is:
$$\boxed{\text{The population is increasing by 3\% each year.}}$$
$$
P = 250000 \cdot (1.03)^z,
$$
where $z$ represents the number of years after the year 2000.
1. Notice that the factor $1.03$ is raised to the power $z$, which means that for each additional year the population is multiplied by $1.03$.
2. Since $1.03$ can be written as $1 + 0.03$, this indicates that the population increases by $0.03$ times (or $3\%$) of its previous value each year.
3. Therefore, the statement "The population is increasing by $3\%$ each year" correctly interprets the factor $1.03$ in the model.
Thus, the correct answer is:
$$\boxed{\text{The population is increasing by 3\% each year.}}$$
