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.
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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

The average rate of change between 1996 and 1997 can be found by evaluating the slope of a secant line passing through the points (6, -164) and (7, -252). Using the formula for slope, we have:

slope = (change in y)/(change in x) = (-252 - (-164))/(7 - 6) = -88

This means that the deficit decreased by an average rate of $88 billion per year from 1996 to 1997. The closest answer choice is C, which says that the deficit decreased by an average rate of $85.5 billion from 1996 to 1997. While this is not an exact match, it is the best choice given the options.

The Table Gives the Yearly U