Question

the relationship between the number of years (x) that have passed and the population (y) for a small town
population count per year
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 the value of x.

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

Step2: Substitute x = 12 into the regression equation.

Substitute \( x = 12 \) into \( y = 1200(1.2)^x \):

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

First, calculate \( (1.2)^{12} \). Using a calculator, \( (1.2)^{12} \approx 8.916 \).
Then, multiply by 1200:

$$ y = 1200 \times 8.916 = 10699.2 $$

Rounding to a reasonable whole number, we get approximately 10699.

Answer:

D. 10,699