The population of a city, y , in thousands of people, measured x years after 1800 can be modeled by the regression equation y is equal to the fraction with numerator 187 point 6 and denominator 1 plus 29 point 4 e raised to the negative 0 point 0 3 x power Which statement best interprets a value in the equation?
Answer
A
The city population in 1800 was 187 comma 600 people.
B
The city population grows by 29 comma 400 people per year.
C
The limiting value of the city population is 187 comma 600 people.
D
The limiting value of the city population is 29 comma 400 people.
Explanation
As x increases, e raised to −0.03x approaches 0. The denominator then approaches 1, so y approaches 187.6 thousand people, or 187,600 people. Therefore, the equation’s limiting population is 187,600 people, as choice C states.
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