Mathematics

  1. If the profit from the sale of x units of a product is P = 105x − 300 − x 2 , what level(s) of production will yield a profit of $1050? (Enter your answers as a comma-separated list.) x = _________ units 2. The total costs for a company are given by C(x) = 5400 + 80x + x 2 and the total revenues are given by R(x) = 230x. Find the break-even points. (Enter your answers as a comma-separated list.) x= __________ units 3. If total costs are C(x) = 900 + 800x and total revenues are R(x) = 900x − x2, find the break-even points. (Enter your answers as a comma-separated list.) x= _____________ 4. For the years since 2001, the percent p of high school seniors who have tried marijuana can be considered as a function of time t according to p = f(t) = 0.17t2 − 2.61t + 52.64 where t is the number of years past 2000.† In what year after 2000 is the percent predicted to reach 75%, if this function remains valid? _______________ 5. Using data from 2002 and with projections to 2024, total annual expenditures for national health care (in billions of dollars) can be described by E = 4.61x2 + 43.4x + 1620 where x is the number of years past 2000.† If the pattern indicated by the model remains valid, in what year does the model predict these expenditures will reach $15,315 billion?