With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year.
A) 120 years
B) 137 years
C) 84 years
D) 270 years
E) 47 years

Question

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by  where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year. ​
A) 120 years 
B) 137 years 
C) 84 years 
D) 270 years 
E) 47 years

Quizplus · Accepted Answer

To find the predicted average life span from 2040 to 2055, we need to find the value of the function for x = 140 to x = 155 (since x = 0 corresponds to 1900 and x = 140 corresponds to 2040).

11ea984b_b06e_4fd0_9029_d109f127fc89_TB4005_11

= -0.000068x^4 + 0.011602x^3 - 0.672492x^2 + 21.069717x + 17.032232

Thus, we need to find the average of the values of the function for x = 140 to x = 155:

{(11ea984b_b06e_4fd0_9029_d109f127fc89_TB4005_11 for x = 140) + (11ea984b_b06e_4fd0_9029_d109f127fc89_TB4005_11 for x = 141) + ... + (11ea984b_b06e_4fd0_9029_d109f127fc89_TB4005_11 for x = 155)}/16

Using a calculator, we get an average of approximately 84 years. Therefore, the answer is C, 84 years.

With the Data for Selected Years from 1920 to 2007