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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.

1

Population Count Per Year

2

3

4

5

6

7

8

Number of Years (x)

Population (v)

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)*

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

Answer 1

To make a prediction using the regression equation \( y = 1,200(1.2)^x \), we will substitute \( x = 12 \) into the equation to find the projected population after 12 years.

Using the equation:

\[ y = 1,200(1.2)^{12} \]

First, we calculate \( (1.2)^{12} \):

\[ (1.2)^{12} \approx 8.9161 \]

Next, we multiply this value by 1,200:

\[ y \approx 1,200 \times 8.9161 \approx 10,699.32 \]

Since population counts are typically whole numbers, we can round this value to 10,699.

Therefore, the best prediction for the town's population after 12 years is:

D. 10,699