Question

The population of a city, y, in thousands of people, measured x years after 1800 can be modeled by the regression equation

y = 187.6/1 + 29.4e^-0.03x

Which statement best interprets a value in the equation?

The city population in 1800 was 187,600 people.
The city population grows by 29,400 people per year.
The limiting value of the city population is 29,400 people.
The limiting value of the city population is 187,600 people.

Answer 1

The regression equation does not provide specific values for the city population in 1800 or the growth rate per year. It does indicate a limiting value for the population as time goes on.

Step-by-step explanation:

The regression equation is y = 187.6/(1 + 29.4e-0.03x). Let's interpret the values in the equation:

• The city population in 1800 was not 187,600 people. The constant term in the equation, 187.6, does not represent the population in 1800.
• The coefficient of the exponential term, 29.4, does not represent the growth rate per year. It is a coefficient that helps determine the shape of the exponential growth curve.
• The exponential term, e-0.03x, represents the population growth or decline over time. As x increases, the term e-0.03x approaches 0, indicating a limiting value for the city population. However, this limiting value is not 29,400 people. It would require solving the equation to find the specific limiting value.

Answer 2

D. The limiting value of the city population is 187,600 people.

Step-by-step explanation:

I'm honestly not sure, but it's based on the 187.6 on top of the equation. Correct on Edge 2021