Keywords:
population, Canadian geese, growth rate
For this case, we must find the population of Canadian geese for the year 2022, taking into account that in 2016 the estimated population of geese was 750 and as additional data, the population of geese has a growth rate of 12% each year.
Then, we started finding the Canadian geese population for 2017, for this we make a rule of three:
750 -----------> 100%
x --------------> 12%
DOnde "x" represents the number of geese that is added to the base population of 2016.
[tex]x = \frac {12 * 750} {100}\\x = 90[/tex]
Thus, the geese population for 2017 is: [tex]750 + 90 = 840[/tex]
We find the population of Canadian geese for the year 2018, following the previous steps since the annual growth rate is constant:
840 -----------> 100%
x --------------> 12%
where "x" represents the number of geese that is added to the base population of the year 2017.
[tex]x = \frac {12 * 840} {100}\\x = 100.8[/tex]
Thus, the geese population for 2018 is: [tex]840 + 100.8 = 940.8[/tex]
We found the population of Canadian geese for the year 2019, following the previous steps since the annual growth rate is constant:
940.8 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that is added to the base population of the year 2018.
[tex]x = \frac {12 * 940.8} {100}\\x = 112.896[/tex]
Thus, the geese population for 2019 is: [tex]940.8 + 112.896 = 1053.696[/tex]
We find the population of Canadian geese for the year 2020, following the previous steps since the annual growth rate is constant:
1053.696 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that adds to the base population of the year 2019.
[tex]x = \frac {12 * 1053.696} {100}\\x = 126.44[/tex]
Thus, the geese population for 2020 is: [tex]1053.696 + 126.44 = 1180.12[/tex]
We found the population of Canadian geese for the year 2021, following the previous steps since the annual growth rate is constant:
1180.12 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that is added to the base population of the year 2020.
[tex]x = \frac {12 * 1180.12} {100}\\x = 141.6[/tex]
Thus, the population of geese for 2021 is:[tex]1180.12 + 141.6 = 1321.7[/tex]
We found the population of Canadian geese for the year 2022, following the previous steps since the annual growth rate is constant:
1321.7 -----------> 100%
x --------------> 12%
[tex]x = \frac {12 * 1321.7} {100}\\x = 158.6[/tex]
Where "x" represents the number of geese that adds to the base population of the year 2021.
Thus, the population of geese for 2022 is: [tex]1321.7 + 158.6= 1480.3[/tex]
ANswer:
The population of Canadian geese by 2022 will be approximately 1480 geese
