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 model to find and interpret the instantaneous rate of change of the U.S. federal deficit (or surplus) in 1995.

A) This model predicts a budget deficit increase of $590.3 billion from 1995 to 1996.
B) This model predicts a budget deficit increase of $81.2 billion from 1995 to 1996.
C) This model predicts a budget deficit decrease of $811.6billion from 1995 to 1996.
D) This model predicts a budget deficit decrease of $81.2 billion from 1995 to 1996.
E) This model predicts a budget deficit decrease of $590.3 billion from 1995 to 1996.

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 model to find and interpret the instantaneous rate of change of the U.S. federal deficit (or surplus) in 1995.
​
A) This model predicts a budget deficit increase of $590.3 billion from 1995 to 1996. 
B) This model predicts a budget deficit increase of $81.2 billion from 1995 to 1996. 
C) This model predicts a budget deficit decrease of $811.6billion from 1995 to 1996. 
D) This model predicts a budget deficit decrease of $81.2 billion from 1995 to 1996. 
E) This model predicts a budget deficit decrease of $590.3 billion from 1995 to 1996.

Quizplus · Accepted Answer

We need to find the instantaneous rate of change of D in 1995, which can be represented as  dD/dt|1995. To find this, we take the derivative of the function D= -290t^3 + 7800t^2 - 55,800t + 114,000 with respect to t and evaluate it at t=5 (since 1995 is 5 years past 1990). 
dD/dt = -870t^2 + 15,600t - 55,800 
dD/dt|1995 = -870(5)^2 + 15,600(5) - 55,800 = -81.2 
This means that in 1995, the deficit was decreasing by $81.2 billion per year, according to the model. So the correct answer is D) This model predicts a budget deficit decrease of $81.2 billion from 1995 to 1996.

The Table Gives the Yearly U