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.
population count per year
number of years (x) | population (y)
1 | 1,440
2 | 1,728
3 | 2,074
4 | 2,488
5 | 2,986
6 | 3,583
7 | 4,300
8 | 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 town’s population after 12 years?
a. 6,020
b. 8,600
c. 8,916
d. 10,699

Explanation:

Step1: Identify the regression equation

Given equation: $y = 1200(1.2)^x$

Step2: Substitute x=12 into the equation

$y = 1200(1.2)^{12}$

Step3: Calculate $(1.2)^{12}$

$(1.2)^{12} \approx 8.9161$

Step4: Compute the final value

$y \approx 1200 \times 8.9161 = 10699.32$ (rounded to nearest integer)

Answer:

D. 10,699