The total public debt D (in trillions of dollars) in the United States at the beginning of each year from 2000 through 2008 can be approximated by the model D = 0.032t2 + 0.21t + 5.6,      0 ≤ t ≤ 8 where t represents the year, with t = 0 corresponding to 2000.† (a) Use the model to complete the table to determine when the total public debt reached or surpassed $7 trillion. t D 0   1   2   3   4   5   6   7   8   The public debt reached or surpassed $7 trillion sometime in 2004.The public debt reached or surpassed $7 trillion sometime in 2005.    The public debt reached or surpassed $7 trillion sometime in 2006.The public debt reached or surpassed $7 trillion sometime in 2007.The public debt reached or surpassed $7 trillion sometime in 2008. (b) Verify your result from part (a) algebraically and graphically. (Round your answer to two decimal places.) t =  (c) Use the model to predict the public debt in 2016. $  trillion

The number (in thousands) of women in the work force as function of the year is shown in the figure below.     Calculate and interpret the following in your case study report. Evaluate f(1983) and f(2011) using the graph. Solve f(year) = 50,000,000 using the graph. Solve f(year) = 43,000,000 using the graph. Estimate f(2014) - f(1994) using the graph. What are the natural domain and range of this function?

The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an explosion in the oil rig Deepwater Horizon, which resulted in the deaths of 11 people and triggered a massive oil spill into the Gulf of Mexico. Estimates of the exact amount of the oil spilled vary based on the source, but it is clearly a function of the number of days n it lasted and the leak rate of the oil, estimated by the United States Geological Service (USGS) to be 504,000 gallons each day! The function u that estimates the amount of oil spilled in n days can be defined as u(n) = 504,000n gallons/day. To find out how much oil spilled the first month (30 days), let n = 30: u(30) = 504,000 (30) U.S. Coast Guard photo a(n) : According to BP's worse-case scenario, the amount of oil spilled in n days can be estimated by the function b(n) = 2.520n million. gallons, while the function r(n) = 441,000n gallons represents the amount of oil that can be recovered in n days. (a) The function a(n) =…

A bucket is filled from a hose that has a constant flow rate. Is the amount of water in the bucket best described by a linear or exponential function of time during the filling process? Explain.