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.

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.
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Quizplus · Accepted Answer

To find the instantaneous rate of change in 1995, we need to find the derivative of the given function.

11eb0d3b_984f_56a3_9790_b124cdc7c152_TB1243_11

= -0.0717t^2 + 2.8376t - 28.2057

Now we can find the instantaneous rate of change (the derivative) at t = 5 (since 1995 is 5 years past 1980):

dD/dt = -0.0717(5)^2 + 2.8376(5)

= -1.7925

Since the coefficient of t^2 is negative, the instantaneous rate of change is decreasing (i.e. the deficit is decreasing) in 1995. The answer is D, as it is the only choice that predicts a decrease in the deficit from 1995 to 1996.

The Table Gives the Yearly U