Modeling with Rational Functions Answers

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 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?

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?

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 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?

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?

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?

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?

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?

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?