Application problems (assessment)

EXERCISES PROBLEMS

(Form A) In the following exercises and problems you will be able to apply models of situa- tions related to the administration of companies using linear, polynomial, exponential and logarithmic functions learned in modules 1, 2 and 3. It correctly uses notation or mathematical terminology. Be sure to include correct mathematical procedures and. provide clear and complete explanations and interpretations Remember to express the solution in the context of the situation. Note: In the event that the result is decimal, you will round it to two decimal places. 1. A company provides its representatives with a car for official use in the company. The company must determine whether to buy or rent the car that will usen. The company has the following options: o Buy the car with an initial disbursement of $50,000, plus 24 fixed monthly payments of $3,500 including insurance. At the end of the 24 months, the car can be sold for $59,400. 0 Rent a car for $2,200 per month plus $0.15 per mile traveled and a one- time payment of $7,500 for two-year auto insurance. The company estimates the average of its trips per month will be 850 miles per month for the next two years. Which option is most convenient for the company in terms of lower costs? (15 points) 2. The number of units sold weekly for a certain product depends on the umountx in dollars invested in advertising and is given by the function y s 70 + 150x 0.3x2. How much should you spend a week onadvertising to get a maximum sales volume? (5 points) 3.A employer pays $3,000 per month ofofce space rent and $1,000 to 12 employ ees, plus a $10 bonus for each unit of work completed by the employee during the month. In addition, the employer has a prot of $18 per unit of work per employee. 0 Suppose an employee completes 300 units in a month. Let's also assume that all employees completed 300 units. Calculates the employer's in come. (5 points) 4.The value and of a cart (in thousands of dollars) can be approximated by the model and , 25(0.85)'where 2' is the number of years since the cart was new. 0 Indicates whether the model represents exponential growth or decline. Jus tify your answer. (5 points) 5 .Si dollars are invested at the end of each year in an annuity that generates interest at an annual rate r, the amount in the accountwill be A dollars after 71 years, where loglAr +1] _ P _ 10g(1+r] If $2,200 is invested each year in an annuity that generates an annual interest of 11%, when will the account be worth $25,000? Round to the nearest tenth. (5 points) Eid ofdoci net