The general form of exponential growth is

\(\displaystyle{y}={y}_{{0}}{e}^{{{k}{t}}}\)

where,

\(\displaystyle{y}_{{0}}=\) initial population

k= constant growth rate

In this question, we have been given the initial population and a constant growth rate which is

\(\displaystyle{y}_{{0}}={3600}\)

k=4.5%=0.045

Substituting the values in equation (1) we have the equation that models the population of the town t years after 2015

\(\displaystyle{y}={3600}{e}^{{{0.045}{t}}}\)

Here we have to calculate the population in 2025 which means the time t = 10 after 2015

\(\displaystyle{y}={3600}{e}^{{{0.045}{\left({10}\right)}}}\)

\(\displaystyle{y}={3600}{e}^{{{0.45}}}\)

\(\displaystyle{y}={3600}\times{1.56}\)

\(\displaystyle{y}={5647.49}\)

\(\displaystyle{y}={5648}\)(approx)

hence, the population in 2025 is y=5648

\(\displaystyle{y}={y}_{{0}}{e}^{{{k}{t}}}\)

where,

\(\displaystyle{y}_{{0}}=\) initial population

k= constant growth rate

In this question, we have been given the initial population and a constant growth rate which is

\(\displaystyle{y}_{{0}}={3600}\)

k=4.5%=0.045

Substituting the values in equation (1) we have the equation that models the population of the town t years after 2015

\(\displaystyle{y}={3600}{e}^{{{0.045}{t}}}\)

Here we have to calculate the population in 2025 which means the time t = 10 after 2015

\(\displaystyle{y}={3600}{e}^{{{0.045}{\left({10}\right)}}}\)

\(\displaystyle{y}={3600}{e}^{{{0.45}}}\)

\(\displaystyle{y}={3600}\times{1.56}\)

\(\displaystyle{y}={5647.49}\)

\(\displaystyle{y}={5648}\)(approx)

hence, the population in 2025 is y=5648