The population growth of a state since 2000 in millions of people is represented by a linear model. Using the trend line, y=0.83x+30

Question

, predict the population, y
, in the year 2030. Let x=30
because the year 2030 is 30 years after the year 2000.(1 point)
Responses

In 2030, the population of the state will be 0.83 million people.
In 2030, the population of the state will be 0.83 million people.

In 2030, the population of the state will be 30.03 million people.
In 2030, the population of the state will be 30.03 million people.

In 2030, the population of the state will be 60.83 million people.
In 2030, the population of the state will be 60.83 million people.

In 2030, the population of the state will be 54.9 million people.

Answer 1

To predict the population in the year 2030 using the given linear model \( y = 0.83x + 30 \), where \( x \) represents the number of years since 2000, we substitute \( x = 30 \):

\[ y = 0.83(30) + 30 \]

Calculating this step by step:

1. Multiply \( 0.83 \) by \( 30 \):

\[ 0.83 \times 30 = 24.9 \]

2. Add \( 30 \) to this result:

\[ 24.9 + 30 = 54.9 \]

Thus, the predicted population in the year 2030 is:

\[ y = 54.9 \text{ million people} \]

The correct response is: In 2030, the population of the state will be 54.9 million people.