The relationship between the number of years x that have passed and the population y for a small town is shown in the table.
Population Count Per Year
Number of Years x 1 2 3 4 5 6 7 8
Population y
14401,440 1,728 2,074 2,488 2,986 3,583 4,300 5,160
Question
A regression equation for this data is y equals 1,200 left-parenthesis 1.2 right-parenthesis Superscript x Baseline.
Based on this data, which value is the ,begin emphasis,best,end emphasis, prediction for the town's population after 12 years?
Answer options with 4 options
A.
6,020
B.
8,600
C.
8,916
D.
10,699
To find the best prediction for the town's population after 12 years using the regression equation, we substitute x = 12 into the equation:
y = 1,200(1.2^x)
y = 1,200(1.2^12)
y ≈ 1,200(8.47)
y ≈ 10,164
Therefore, the best prediction for the town's population after 12 years is approximately 10,164.
The correct answer is not provided in the answer options.