Modeling with Rational Functions Answers

A scientist has 40 liters of a 50% acidic solution. She adds a 20% acidic solution to create a mixture that has been diluted to have 30% acidity. The graph models the percent of acidity in the final mixture. How many liters of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture?

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?

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?

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 function yields the average cost in dollars per cup of lemonade made by Lincoln at his lemonade stand when he makes x cups of lemonade. Which statement best fits the situation modeled by the function?

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?

Sarah plans to sell homemade birdhouses at the local craft fair. She spent $90 on new tools and estimates that she spends $6 in materials for each birdhouse. Which rational function models the average cost per birdhouse, y, in dollars of building x birdhouses?

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?

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 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?