The securities industry experienced dramatic growth in the last two decades of the 20th century. The following models for the industry's revenue R and expenses or costs C (both in billions of dollars) were developed as functions of the years past 1980 with data from the U.S. Securities and Exchange Commission's 2000 Annual Report (2001). and . Use the models to predict the profit for the securities industry in 2009. Round your answer to two decimal places.

Question

The securities industry experienced dramatic growth in the last two decades of the 20th century. The following models for the industry's revenue R and expenses or costs C (both in billions of dollars) were developed as functions of the years past 1980 with data from the U.S. Securities and Exchange Commission's 2000 Annual Report (2001).  and  . Use the models to predict the profit for the securities industry in 2009. Round your answer to two decimal places. ​

Quizplus · Accepted Answer

To find the profit, we subtract the expenses from the revenue: P = R - C. 
Using the given models, we have: 
R = 0.266t^3 - 3.77t^2 + 17.7t + 67.8 
C = 0.184t^3 - 3.01t^2 + 16.6t + 33.4 
where t represents the years past 1980. 
To find the profit in 2009, we substitute t = 29 into the models: 
R(29) = 0.266(29)^3 - 3.77(29)^2 + 17.7(29) + 67.8 = 386.77 
C(29) = 0.184(29)^3 - 3.01(29)^2 + 16.6(29) + 33.4 = 261.73 
P(29) = R(29) - C(29) = 125.04 
Therefore, the profit for the securities industry in 2009 is approximately $125.04 billion. The correct answer choice is D.

The Securities Industry Experienced Dramatic Growth in the Last Two