1. Mrs. Galicia is building a chicken farm in 2021 with an initial population of 3750 chickens. The farm grows at a rate of 2.15% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2021. (b) Estimate the population of the town in 2036.
show plug in step before using calculator Answer:

The exponential growth model is given by the equation, [tex]y=y_oe^{rt}[/tex], where y is the population after t years, y₀ is the initial population, r is the rate of growth, and t is the time.

As it is given that the initial chicken population in the year 2021 is 3750, while the rate at which the population is increasing is 2.15% annually.

A.) The exponential growth model to write an equation that estimates the population t years after 2021.

The exponential growth model can be written as,

[tex]y=y_oe^{rt}\\\\y=3750e^{0.0215t}[/tex]

B.) The population of the town in 2036,

As the population is increasing for the next 15 years(2036-2021). Therefore, The population of the town in 2036 can be written as,

[tex]y=3750e^{0.0215t}\\\\y=3750e^{0.0215\times 15}\\\\y= 5177.1558\approx 5177[/tex]

Hence, the population of the chicken after 15 years in 2036 will be 5177.

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