In one year, the population will increase by 9% of its original size, that is, [tex]180,000(0.09) + 180,000 = 180,000(0.09 + 1) = 180,000(1.09)[/tex], which is the population multiplied by 1.09.
The next year, the population will be again multiplied by 1.09: [tex]180,000(1.09)(1.09)[/tex].
We can write the trend as an equation:
P = 180000(1.09)^n, where n is the number of years and P is the population after n years.
To find the number of years for for the population to reach 300,000, we can substitute 300,000 into our equation and solve for n.
[tex]P = 180000^n \\
300000 = 180000(1.09)^n \\
\frac{5}{3} = 1.09^n \\
\log_{1.09} \frac{5}{3} = n \\ \\
n = 5.9[/tex]
