Final answer:
Life expectancy in the U.S. from 2000 to 2016 can be modeled with a polynomial function, and graphing this function can shed light on trends during that period. The average rate of change in life expectancy is calculated using the values given by the model at the start and end of the period. Various factors affect life expectancy, causing trends to differ between countries and times.
Step-by-step explanation:
The student asked about the life expectancy in the United States and its average rate of change from the year 2000 to 2016 using a polynomial function to model this change. This falls under the subject of Mathematics, specifically polynomial functions and their application in real-life situations. In part (a), the student is tasked with graphing the function for the years from 2000 to 2016, which can be done using graphing technology such as a graphing calculator or software. The behavior of this graph within this interval will likely show either an increase or decrease in life expectancy over time.
To address part (b) of the question, the average rate of change of life expectancy can be found by taking the difference in the life expectancy values at t=0 and t=16 and then dividing by 16. Essentially, it is the slope of the secant line that connects the points on the graph corresponding to the years 2000 and 2016. This gives an idea of the overall trend in life expectancy change during this period. By interpreting data from various reference points, it becomes clear that life expectancy is influenced by multiple factors, including national wealth, healthcare expenditure, nutrition, and social conditions. Comparing different countries and times, life expectancy can vary greatly. Over recent years, the life expectancy in the U.S. has faced a downward trend, a concern that points toward social and economic issues within the country.