In the year 2000, the total amount of consumer loans in the United States topped
ID: 2457459 • Letter: I
Question
In the year 2000, the total amount of consumer loans in the United States topped $550 billion dollars. According to the Archival Federal Reserve Economic Data report, the total amount of consumer loans for the United States can be approximated by the function L(t) = 0.286t^2 - 3.669t + 24.475 where t is the number of years after 1950 and L(t) is given in billions of dollars. Evaluate and interpret the instantaneous rate of change in the total amount of consumer loans in the United States in 2020.Explanation / Answer
In the year 2000, the total amount of consumer loans in the United States topped $550 billion dollars. The total amount of consumer loans growth approximated function is
L(t) = 0.286 t2 - 3.669 t + 24.475 where t is the number of years after 1950 and L(t) is given in billions of dollars.
The rate of change in the total amount of consumer loans in the United States in 2020 is
L(70) = 0.286 (70)2 - 3.669 * 70 + 24.475
=> L(70) = 11.69 % rate
Answer : a. The total amount of consumer loans in the United States is expected to grow in 2020 at a rate of 11.69 billion dollars.