Modeling with Rational Functions Answers

The teachers’ editions of a statistics textbook sell for $150 each, and students’ editions of the book sell for $50 each. Which function can be used to find the average cost per book if two teachers’ editions and x students’ editions are purchased?

A 22,800-gallon swimming pool is being filled by four hoses. Water flows through each hose at a rate of 300 gallons per hour. How many hours will it take to fill the pool?

The function yields the average cost in dollars for a company to produce x calendars. Which statement best fits the situation modeled by the function?

For a fixed amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. The function relates the volume in cubic inches and pressure in pounds per square inch of a gas. What is the volume when the pressure is 900 pounds per square inch?

A pharmacist has 80 milliliters of a 25% saline solution. Which expression can be used to find the percentage concentration of the final solution if she adds x milliliters of a 10% saline solution?

Craig bought a treadmill for $400. He estimates that the annual costs to maintain the machine will be $36. Which rational function yields the average annual cost in dollars of owning the treadmill for x years?

The function models y, the average annual cost in dollars of owning a car for x years. Which statement best explains why the graph of should have a vertical asymptote at x = 0?

Louis plans to buy a new washing machine. The washing machine costs $560 and has an estimated annual operating cost of $48. Which rational function models the average annual cost in dollars of owning the washing machine for x years?

The Watkins family is trying to decide which kind of in-ground pool to install. They are determining whether to put in a saltwater pool or a basic chlorine pool. The graphs below model the average annual cost of owning each type of pool after t years. If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do you know?

Frank joined a fitness club. He paid a $50 registration fee, and dues are $12 per month. Which expression can be used to find the average monthly cost of an x-month membership at the club?

Greg plans to purchase a bicycle. Bike A costs $270 and has an expected maintenance cost of $36 per year. Bike B costs $360 and has an expected maintenance cost of $20 per year. Which statement is true based on the average annual cost of each bike?

The game commission introduces 200 white-tailed deer into a newly acquired national game and wildlife park. The population of the herd is modeled by the graph of the rational function below, where time is measured in years. Which statement about the population is true?

Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A charges 4% interest over 6 years. Plan B charges 5% interest over 4 years. The formula can be used to calculate the monthly payment, m, where P is the principle amount borrowed, r is the interest rate expressed as a decimal, and t is the time of the loan, in years. Which statement best compares the plans?

A pharmacist has 80 milliliters of a 30% saline solution. The graph shows the percentage concentration after adding x milliliters of a 10% saline solution. Which statement is true about the graph of the function?

The function relates y, the time in hours that it takes Michael to travel to his grandparents’ house, to x, his average speed in miles per hour. What does the number 60 in the function represent?

The function yields the average cost in dollars for a company to produce x copies of a comic book. Which statement best fits the situation modeled by the function?