The table gives the yearly U.S. federal budget deficit (as a negative value) or surplus (as a positive value) in billions of dollars from 1990 to 2004.

Source: Budget of the United States Government
Assume the federal budget deficit (or surplus) can be modeled with the function , where D is in billions of dollars and t is the number of years past 1980. Use the data to find an average rate of change that approximates the instantaneous rate in 1996.

A) The budget deficit increased by an average rate of $85.5 billion from 1996 to 1997.
B) The budget deficit increased by an average rate of $831.3 billion from 1996 to 1997.
C) The budget deficit decreased by an average rate of $85.5 billion from 1996 to 1997.
D) The budget deficit decreased by an average rate of $83.1 billion from 1996 to 1997.
E) The budget deficit decreased by an average rate of $469.9 billion from 1996 to 1997.

Question

The table gives the yearly U.S. federal budget deficit (as a negative value) or surplus (as a positive value) in billions of dollars from 1990 to 2004. ​

Source: Budget of the United States Government
Assume the federal budget deficit (or surplus) can be modeled with the function  , where D is in billions of dollars and t is the number of years past 1980. Use the data to find an average rate of change that approximates the instantaneous rate in 1996.
​
A) The budget deficit increased by an average rate of $85.5 billion from 1996 to 1997. 
B) The budget deficit increased by an average rate of $831.3 billion from 1996 to 1997. 
C) The budget deficit decreased by an average rate of $85.5 billion from 1996 to 1997. 
D) The budget deficit decreased by an average rate of $83.1 billion from 1996 to 1997. 
E) The budget deficit decreased by an average rate of $469.9 billion from 1996 to 1997.

Quizplus · Accepted Answer

To approximate the instantaneous rate of change in 1996, we need to calculate the average rate of change between 1995 and 1997 because we can assume that the deficit varied smoothly between those years.

From the table, we can see that the deficit in 1995 was -164.0 billion and in 1997 was -22.6 billion.

Plugging these values into the formula, we get:

average rate of change = (D(1997) - D(1995))/(1997-1995) = (-22.6 - (-164.0))/2 = 70.7

This means that, on average, the deficit decreased by 70.7 billion dollars per year from 1995 to 1997. However, we're interested in the change specifically for 1996, so we need to figure out whether the deficit increased or decreased from 1996 to 1997.

From the table, we can see that the deficit in 1996 was -107.4 billion, and in 1997 was -22.6 billion. This means that the deficit decreased from 1996 to 1997, so the answer is C: The budget deficit decreased by an average rate of $85.5 billion from 1996 to 1997.

The Table Gives the Yearly U