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?

CheemnCatelvew

CheemnCatelvew

Answered question

2021-02-09

In 2015, there were 3,600 people living in a small town. Every year, the population grows by 4.5%. Write the exponential equation that represents the town's population t years from now, in 2015. Then, how about using your equation to predict the population in 2025?

Answer & Explanation

izboknil3

izboknil3

Skilled2021-02-10Added 99 answers

In its most basic form, exponential growth is
y=y0ekt
where,
y0= initial population
k= constant growth rate
In this question, we have been given the initial population and a constant growth rate which is
y0=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
y=3600e0.045t
Here we have to calculate the population in 2025 which means the time t=10 after 2015
y=3600e0.045(10)
y=3600e0.45
y=3600×1.56
y=5647.49
y=5648(approx)
hence, the population in 2025 is y=5648

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