ECON1003 Graded Individual Assignment [Read-Only] [Compatibility Mode] - Microsoft Word PAGE LAYOUT REFERENCES MAILINGS REVIEW VIEW Problem Set A (1) For the function f(x) =1- (x+2)2 : find the following: (1) f (-x) (ii) f(x+ k) (2) The price p (in dollars) and the quantity q sold of a certain product obey the demand equation q =800-20p and 0 5 p = 40 (i) Express the revenue R as a function of q. (ii) What is the revenue if 20 units are sold? (iii) What quantity q maximizes revenue? What is the maximum revenue? (iv) What price should the company charge to maximize revenue? (v) What price should the company charge to earn at least $3500 in revenue? (3) You are an accountant for a manufacturer of radios. The demand function for the tablets is p =40-4x- where x is the number of tablets produced in millions. It costs the company $15 to make a tablet. (i). Write an equation for the manufacturer's profit as a function of the number of tablets produced. (ii). The company currently produces 1 million tablets and makes a profit of $21,000,000, but you would like to scale up production a bit. What greater number of tablets could the company produce to yield the same profit?AGE LAYOUT REFERENCES MAILINGS REVIEW VIEW Problem Set B (1) (a) Solve the following: (1) 2*-6 8 (ii) log, (x+3) =1-log; (x-1) (b) The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per year (i) Assuming that this growth rate continues, derive a model to represent the population P (in billions of people) in year t. (ii) From the model derive in (1), approximately when will the population of the world be 11.2 billion people? (2) The number of women in the workforce, based on data and projections from 1950 to 2050, can be modeled by a linear function. The number was 18.4 million in 1950 and is projected to be 81.6 million in 2030. Let x represent the number of years after 1950. (i). What is the slope of the line? (ii). What is the average rate of change in the number of women in the workforce during this time period? 2 (iii). Use the slope from part (i) and the number of millions of women in the workforce in 1950 to write the equation of the line.AGE LAYOUT REFERENCES MAILINGS REVIEW VIEW Problem Set C 2x + 3 (1) Find the domain of the function H(x) = x3 -4x (2) Solve the following (i) |10-3x 17 (1i) x2 - 6x 2 13. (3) Showing all your working, find the solution set which describes the area shown in purple below. 10 V 6 -1 0 2 6 7 9 10Problem Set D (1) If you have been hired at an annual salary of $23,000 and expect to receive annual increases of 5%, what will your salary be when you begin your seventh year? (2) Determine the inverse of the function f (x) = 3x 2x - 5 (3) Ladders used by fruit pickers are typically tapered with a wide bottom for stability and a narrow top for ease of picking. If the bottom rung of such a ladder is 49 inches wide and the top rung is 19 inches wide. Stating explicitly the formulae used, determine: (i) How many rungs does the ladder have if each rung is 2.5 inches shorter than the one below it? (ii) How much material would be needed to make the rungs for the ladder described