The table gives the percent of the population of a certain city that was foreign born in the given year. Find a cubic function that best fits the data where x is the number of years after 1900 and y is equal to the percent. By trial and error, estimate the year the model predicts that the foreign-born population will be 100%. Round numerical values in your answer to three decimal places.
A) Foreign born population will be 100% in 1965.
B) Foreign born population will be 100% in 1975.
C) Foreign born population will be 100% in 1975.
D) Foreign born population will be 100% in 1965.
E) Foreign born population will be 100% in 1985.

Question

The table gives the percent of the population of a certain city that was foreign born in the given year. Find a cubic function that best fits the data where x is the number of years after 1900 and y is equal to the percent. By trial and error, estimate the year the model predicts that the foreign-born population will be 100%. Round numerical values in your answer to three decimal places. ​  ​
A) Foreign born population will be 100% in 1965. 
B) Foreign born population will be 100% in 1975. 
C) Foreign born population will be 100% in 1975. 
D) Foreign born population will be 100% in 1965. 
E) Foreign born population will be 100% in 1985.

Quizplus · Accepted Answer

By trial and error, a cubic function that best fits the given data is y = 0.001x^3 - 0.131x^2 + 6.157x - 69.327. To determine the year when the foreign-born population will be 100%, we need to find the x-intercept (when y = 0.100). Using a graphing calculator or software, we find that the x-intercept is approximately 75.447, which corresponds to the year 1975. Therefore, the correct choice is C.

The Table Gives the Percent of the Population of a Certain