We know that the initial population is 10,000, since the popuation grows at a rate of 1.2% yearly the first year the population will be:
[tex]\begin{gathered} 10,000+10,000(0.012)=10,000(1+0.012) \\ =10,000(1.012) \end{gathered}[/tex]Remembering that the population growth is given as:
[tex]y=ab^x[/tex]where y is the final population, a is the initial population and b is the growth factor we have in this case that:
[tex]y=10,000(1.012)^x[/tex]Then, after three years we will have:
[tex]\begin{gathered} y=10,000(1.012)^3 \\ =10364.34 \end{gathered}[/tex]Therefore after three years we will have approximately 10364 people.
