According to the Association of American Railroads, Class I freight railroads are the line-haul freight railroads with 2006 operating revenue in excess of $346.8 million. Let F = F(t) denote the freight revenue in billions of dollars of Class I railroads in year t. In 2005, Class I railroads had a freight revenue of $44.5 billion. In 2007, the revenue was $52.9 billion. Calculate the average rate of change per year in F from 2005 to 2007. billion dollars per year Explain in practical terms what this means. O This is the value, in billions of dollars, by which the freight revenue for Class I railroads decreased, on average, over this two-year period. O This is the value, in billions of dollars, describing the average difference in freight revenue for Class I and Class II railroads. O This is the number of years, on average, it takes for the freight revenue for Class I railroads to decrease by 2 billion dollars. O This is the number of years, on average, it takes for the freight revenue for Class I railroads to increase by 2 billion dollars. O This is the value, in billions of dollars, by which the freight revenue for Class I railroads increased, on average each year, over this two-year period.

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) =…

Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with α=0.1.

Each month, Uncle Joe’s Auto Parts uses exponential smoothing (with α = 0.25) to predict the number of barrels of brake fluid that will be sold during the next month. In June Uncle Joe forecast that he would sell 37 barrels of brake fluid during July. Uncle Joe actually sold 43barrels in July. What is Uncle Joe’s forecast for brake fluid sales in August and September?