Question

The population of a small town was 3,600 people in the year 2015. The population increases by 4.5% every year. Write the exponential equation that models the population of the town t years after 2015. Then use your equation to estimate the population in the year 2025?

Exponential models
ANSWERED
asked 2021-02-09
The population of a small town was 3,600 people in the year 2015. The population increases by 4.5% every year.
Write the exponential equation that models the population of the town t years after 2015.
Then use your equation to estimate the population in the year 2025?

Answers (1)

2021-02-10

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 \(y=5648\)

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