Answer:
D. the vertex tells us that 12 years after 2000, 46594 people were below the poverty level.
e. 9 years after 2000 and 15 years after 200, 44 million people were below the poverty line.
f. range is [21646, 46, 594 ]
Step-by-step explanation:
Part D:
Let us graph the function and try to answer our questions from it.
From the graph, we see that the vertex of the function is at (12, 46 594). What does it tell us? It tells us that when t = 12 (meaning 12 years after 2000) n = number of people below poverty level = 46 594.
In simple words, this means " the vertex tells us that 12 years after 2000, 46594 people were below the poverty level. "
Part E:
Now when were there 44 million people (i.e. n = 44 000) below the poverty line?
To find out we draw a horizontal (blue) line that passes through n = 44 000 and see where it intersects. The x-coordinate of the intersection point is the value of t we are looking for.
Where does the blue line intersect the parabola? We can easily see that it intersects at about t = 9 (9 years after 2000) and at t = 15 ( 15 years after 2000).
Therefore, 9 years after 2000 and 15 years after 200, 44 million people were below the poverty line.
Part F:
We draw two vertical lines ( green and purple ) at t = 3 and t = 18 and see where they intersect the parabola. The y-coordinate of the point of intersection gives the value the function takes at these two points. If we restrict our function to only between t = 3 and t = 18, how will the value of n be restricted?
The answer is the following.
We find the highest and the lowest value of the function (n) in the interval between t = 3 and t = 18.
The highest value the function takes is n = 46 594 and the lowest value it takes is n = 21 646; therefore, the range of the function is [21 646, 46 594]