Answer:
common ratio: 1.155
rate of growth: 15.5 %
Step-by-step explanation:
The model for exponential growth of population P looks like: [tex]P(t)=P_i(1+r)^t[/tex]
where [tex]P(t)[/tex] is the population at time "t",
[tex]P_i[/tex] is the initial (starting) population
[tex](1+r)[/tex] is the common ratio,
and [tex]r[/tex] is the rate of growth
Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:
[tex]P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\[/tex]
This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155
We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:
[tex]1+r=1.155273\\r=1.155273-1=0.155273[/tex]
So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %
