Question

the relationship between the number of years (x) that have passed and the population (y) for a small town is shown in the table.

number of years (x)	1	2	3	4	5	6	7	8
population (y)	1,440	1,728	2,074	2,488	2,986	3,583	4,300	5,160

a regression equation for this data is y = 1,200(1.2)^x.
based on this data, which value is the best prediction for the towns population after 12 years?
a. 6,020
b. 8,600
c. 8,916
d. 10,699

Explanation:

Step1: Identify the regression equation and value of x

The regression equation is $y = 1200(1.2)^x$, and we want to find the population after 12 years, so $x = 12$.

Step2: Substitute x into the equation

$y=1200\times(1.2)^{12}$.
First, calculate $(1.2)^{12}\approx8.9161$.
Then, $y = 1200\times8.9161 = 10699.32$.

Answer:

D. 10,699