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

the relationship between the number of years (x) that have passed and the population (y) for a small town is shown in the table.\n| number of years (x) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |\n| population (y) | 1,440 | 1,728 | 2,074 | 2,488 | 2,986 | 3,583 | 4,300 | 5,160 |\na regression equation for this data is y = 1,200(1.2)^x.\nbased on this data, which value is the best prediction for the towns population after 12 years?\na. 6,020\nb. 8,600\nc. 8,916\nd. 10,699

the relationship between the number of years (x) that have passed and the population (y) for a small town is shown in the table.\n| number of years (x) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |\n| population (y) | 1,440 | 1,728 | 2,074 | 2,488 | 2,986 | 3,583 | 4,300 | 5,160 |\na regression equation for this data is y = 1,200(1.2)^x.\nbased on this data, which value is the best prediction for the towns population after 12 years?\na. 6,020\nb. 8,600\nc. 8,916\nd. 10,699

Answer

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