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Business: Online Advertising Revenue Two niche social networking companies, one for financial advisors and one for accountants, generate revenue from rich media advertisements. The function F(x)=3x2+15x models the revenue (in millions of dollars) for the financial advisors network for the years 2007 to 2012. The function A(x)=x2+9x models the revenue (in millions of dollars) for the accountants network for the years 2007 to 2012 . The ratio A(x)F(x) is a measure of the size of F(x) relative to A(x). For example, if A(x)F(x)=3, then F(x)=3A(x) and you can see that F(x) is three times the size of A(x). That is, the revenue realized by the financial advisors network is three times the revenue realized by the accountants network. (Assume x is the number of years from January 1, 2007.) a. How does the revenue of the financial advisors network compare to that of the accountants niche in 2011 ? b. Write an expression for the rate at which the ratio of revenues changes as the number of years from 2007 changes. c. At what rate is the ratio changing in the year 2011 ? d. Interpret the value you obtained in part c. Writing the value as a decimal number over 1 will help you to do so. 41. Business: Marginal Revenue A manufacturer of ceramic vases has determined that her weekly revenue and cost functions for the manufacture and sale of x vases are R(x)=95x0.08x2 dollars and C(x)=1,200+35x0.04x2 dollars, respectively. Given that profit equals revenue minus cost, a. find the marginal revenue, marginal cost, and marginal profit functions. b. estimate the revenue realized by selling the 601st vase and the 900th vase. What seems to be happening? c. estimate the cost incurred by producing the 601st vase and the 900th vase. What seems to be happening? d. estimate the profit realized by producing the 601st vase and the 900th vase. What seems to be happening? 3. Business: Marginal Profit The publisher of a recently released biography book expects that over the first 15 months after its release, the monthly profit can be approximated with the model P(t)=t2+10200+500t10t2 where P is in thousands of dollars and t is in months from the time of release. a. Derive a model that gives the marginal profit of the book. b. Specify and interpret the expected marginal profit 5 months after release. c. Specify and interpret the expected marginal profit 10 months after release. d. Offer a mathematical argument to demonstrate that from month 3 after release, the monthly profit realized from the sales of the book decreases steadily