Answer:
common ratio: 1.155
rate of growth: 15.5 %
Step-by-step explanation:
The model for exponential growth of population P looks like: 
where
is the population at time "t",
is the initial (starting) population
is the common ratio,
and
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:
![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\\](https://tex.z-dn.net/?f=P%28t%29%3DP_i%281%2Br%29%5Et%5C%5C13000%3D2300%2A%281%2Br%29%5E%7B12%7D%5C%5C%5Cfrac%7B13000%7D%7B2300%7D%20%3D%20%281%2Br%29%5E12%5C%5C%5Cfrac%7B130%7D%7B23%7D%20%3D%20%281%2Br%29%5E%7B12%7D%5C%5C1%2Br%3D%5Csqrt%5B12%5D%7B%5Cfrac%7B130%7D%7B23%7D%20%7D%20%3D1.155273%5C%5C)
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:

So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %
Answer:
0.923
Step-by-step explanation:
There are 13 total marbles. (12 Purple Marbles + One Blue Marble)
The total events are 13 and the number of preferred events is 12.
≈ 0.923
So there should be a 0.923 chance that a purple marble is picked.
Answer:
x=i or no solution exists depending on the user's grade
Step-by-step explanation:
f(x) = 2x^2-5
-7 = 2x^2-5
-2 = 2x^2, x^2=-1, x=i
Answer: 69/15=4 and remainder 9
Step-by-step explanation: Since 15 x 4 = 60, 15 can't go into 9 so 9 in the leftover