Math 1320 Name:D. WilsonExam #1DWednesday, September 17, 2008Show all work for partial credit. Good luck!#1 /24#2 /20#3 /16#4 /20#5 /20Total /100You have Exam # .If I do not receive this exam by the end of class, you will receive ascore of zero.1. The demand equation for a product is q = −40p + 3960 items, where p is the price peritem, in dollars.(a) (6 points) Write the revenue function, and include the units.Recall the revenue is price x quantity.(b) (6 points) What price will maximize the reve nue? Include the units.(c) (6 points) What is the maximum revenue? Include the units.(d) (6 points) How many items will be sold when the revenue is maximized?2. The Audubon Society at Enormous State University is planning its annual fund-raising“Eatathon.” The society will incur a marginal cost of 24¢ per pasta serving, and a fixedcost of $370 cost for renting the facility. The society will charge students 75¢ per pastaserving. Let x represent the number of pasta servings.(a) (5 points) Find the cost func tion. Include the units.(b) (5 points) Find the revenue function. Include the units.(c) (5 points) Find the profit function. Include the units.(d) (5 points) How many servings must the university sell in order to break even?Round the answer to the nearest pasta serving.3. (a) (10 points) Find the equation of the line passing through the points(3, −4) and (−1, 0).(b) In 2004, the Texas Bureau of Economic Geology published a study on the economicimpact of using technology to extract additional oil from fields that have reachedthe end of their conventional economic life. A table (which is not shown) gave theapproximate number of jobs for the citizens of Te xas that would be created at variouslevels of recovery.The regression line equation tells us that y(x) = .14x + 0.6 million jobs will be createdif x percent of oil is recovered.(6 points) Write a sentence that interprets the slope of the line.4. (20 points) Graph the function on the axes provided.f(x) =√−x if − 4 ≤ x < 0−2x + 1 if 0 < x ≤ 45. Consider the function f(x) = 5 − 6x2.(a) (3 points) Find f (4).(b) (6 points) Find and simplify the expression f(x + h).(c) (8 points) Find and simplify the expressionf(x + h) − f(x)h.(d) (6 points) Let f (x) = 5 − 6x2and g(x) = x5. Find and simplify