Econ 289 Assignment 2 (Sections 4.1-4.5) Questions Solve all questions, showing your work in reasonable detail. Finish your calculations: when the results can be reduced to numbers, calculate those numbers. The purpose of the assignment is to help you learn the material in this course; therefore, you are expected to use only the methods and concepts that are specific to this course. Submit the answers in only ONE file, preferably PDF, in Blackboard. 1 ) If tex) = 20 vx , show that for any real number to f ( t x ) = Vit ( x ) 2) Consider the function f ( x ) = 2x" - 3. calculate f ( -1) , f(a-1), f(*), and flux) 3) Find the domains of the following functions: a ) t ( x ) = 1 x 2 - x + 2 b ) f ( x ) = V X - 1 ( ) f ( x ) = 4 x 2 4 ) The cost of producing x units of a product is C (x ) = 10x2+ 50x+ 400. How much does it cost to produce the 11-th unit? How much does it cost to produce then-th unit ? 5 ) Find the slopes of the lines passing through the following points : by (3, 4 ) and (-1 , 5) 6) (2 , - 3 ) and ( 7, 8 ) ( ) ( - 2, -1 ) and (0, 0)6) Determine the equations of the following straight linesand draw the lines on separate graphs a) L passes through ( 2, 3) and has slope=-) 6 ) LZ passes through (-2 , 1 ) and ( 1, 2 ) ( ) La passes trough (4, D) and (0, 6) d ) Ly passes through (a. D ) and ( 0, b), a to 7) Sketch in the xy-plane the set of all pairs of numbers ( x, y ) that satisfy all the following three inequalities : 4 x + 5y = 20, X20, and y20 9) Find the equilibrium price ( P) and quantity demanded and supplied for the following model of supply and demand ( Hint: equilibrium is when the quantity demanded, D, is equal to the quantity supplied, 5.) D= 49- -P , and S = 10+3P 9 ) The cost of producing quantity x of a commodity is a linear function of x. it has been determined that go units were produced at a total cost of $500, and 50 units at a cost of $ 300. Calculate the cost of producing 120 units.10) Many assets such as cars and furniture depreciate ( loose value ) following a linear function of time, each year Loosing a fixed percentage of the initial value . a Suppose the value of a car that initially costs $ 25, Do0 depreciates by 7% of its original value each year. Find a formula for its value P(t) aftert years. b) if a TV set is completely depreciated after 12 years ( linear depreciation ) and its initial value is $800, find a formula for its value after years, W ( + )