Lesson 6a – Practice Problems - Scottsdale Community College ...

Lesson 6a - Exponents and Rational FunctionsPractice Problems6. Solve each of the following rational equations algebraically (also called symbolically).Check your work by plugging the value(s) back into the equation or by graphing.a) b)c) d) 6e) f)Scottsdale Community College Page 256 Intermediate Algebra

Lesson 6a - Exponents and Rational FunctionsPractice Problems7. Mr. Ewald decides to make and sell Left Handed Smoke Shifters as a side business. Thefixed cost to run his business is $250 per month and the cost to produce each Smoke Shifteraverages $8. The Smoke Shifters will sell for $19.95.8x 250The function A(x) gives the average cost (in dollars) per hat when x hats arexproduced.a) Determine A (1), and write a sentence explaining the meaning of your answer.b) Complete the table below.x 1 2 3 4 5A (x)c) Determine A (10), and write a sentence explaining the meaning of your answer.d) How many Smoke Shifters must be produced in order to reduce the average cost to $15per hat?e) Give the equation of the horizontal asymptote of A (x), and write a sentence explainingits significance in this situation.Scottsdale Community College Page 257 Intermediate Algebra

Lesson 6a - Exponents and Rational FunctionsPractice Problems8. Harkins Theaters offers $1.50 soft drink refills every time you bring your 2013 HarkinsLoyalty Cup to the theater. You can purchaser the Loyalty Cup for $5.1.5x 5The function C(x) gives the average cost (in dollars) per refill with the LoyaltyxCup, where x is the number of soft drink refills purchased.a) Determine C (1), and write a sentence explaining the meaning of your answer.b) Complete the table below.x 1 2 3 4 5C (x)c) How many refills must you purchase in order to reduce the average cost to $2 per refill?d) Give the equation of the horizontal asymptote of C (x), and write a sentence explainingits significance in this situation.Scottsdale Community College Page 258 Intermediate Algebra

Lesson 6a - Exponents and Rational FunctionsPractice Problems9. An application of a rational function is T = (AB)/(A+B),which gives the time, T, it takes fortwo workers to complete a particular task where A & B represent the time it would take foreach individual worker to complete the identical task.a) The monthly reports are due and the department manager has decided to try andaccelerate the completion of the report by assigning a team of two workers the task. Maryhas completed the monthly reports in an average of 6 hours over the past few months.John, who had worked in Mary's capacity prior to a change in assignments, used tocomplete the task in 8 hours. How quickly will Mary and John finish the report if theywork together? In this problem, Mary = A = 6 and John = B = 8.b) The very next month, both Mary and John are out sick. The manager knows that Skip cando the reports in 12 hours working alone, but the manager needs the work done in 4hours. He needs to choose a staff member to work with Skip. How quickly would theother staff member have to complete the report working alone if the two hope tocomplete the report in 4 hours?Let A = 12 (Skip's time)Let T = 4c) Sara takes 3 hours longer to paint a floor than it takes Katie. When they work together, ittakes them 2 hours. How long would each take to do the job alone?Sara = A = (X+3) and Kate = B = XScottsdale Community College Page 259 Intermediate Algebra

Lesson 6a - Exponents and Rational FunctionsPractice ProblemsScottsdale Community College Page 260 Intermediate Algebra