Modeling with Rational Functions Answers

Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour? y = x/6.4y = x/160y = 6.4/x✔ y = 160/x

What does the number 160 represent in the rational function that models the situation?

Colleen plans to start a small business by making and selling skirts. A sewing machine costs $250, and she estimates that she will spend $15 on materials for each skirt.Which expression represents Colleen’s total costs, in dollars, for making x skirts?✔ 250 + 15x250x + 15250(15x)(250 + x)15

Which rational function models the average cost per skirt, y, in dollars, for making a total of x skirts?

The total cost of a vacation to a rain forest includes a fee of $560 for the tour guide, plus $630 per person.The function models the average cost per person, in dollars, when x people go on the vacation.What is the horizontal asymptote of the function?y =

Why does it make sense in this situation that the function has this horizontal asymptote?

A horse owner has 50 lbs of hay that is 6% protein by weight. He adds x lbs of oats that is 12% protein by weight. The function models the percent of protein, y, in the final mixture of feed.What is the y-intercept of the function that models the percent of protein in the final mixture?The y-intercept is

What does the y-intercept represent in this situation?

For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3.Which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi? y = 20xy = 18,000xy =20/x✔ y =18,000/x

What would the volume of the gas be if the pressure is increased to 40 psi? in.3

If the volume of the gas increases from 600 to 800 in.3, by how much does the pressure change?✔ It decreases by 7.5 psi.It decreases by 22.5 psi.It increases by 7.5 psi.It increases by 22.5 psi.

Which function models situation?

How much Active Mix should she add in order to have a trail mix containing 30% dried fruit? lbs

When you own a pet, there are one-time costs, such as a leash, and continuing costs, such as food. Suppose the one-time costs for owning a small dog are $180, and the continuing costs are $400 per yearWhich function models the average annual cost of owning a small dog for x years?f(x) = x/(180 + 400x)f(x) = x/(180x + 400)✔ f(x) = (180 + 400x)/xf(x) =(180x + 400)/x

The average annual cost of owning a small dog for 10 years is $.

The function models the average annual cost of owning a cat for x years. On average, which pet costs more per year over a 10-year period?the small dog✔ the catthe costs are the same

On average, how much more is the total cost of owning a cat for 10 years than owning a small dog for 10 years? $ ⇒ 960

The Gordon family plans to buy a TV. One TV has a purchase price of $330 and an estimated yearly operating cost of $14. The other has a purchase price of $369 and an estimated yearly operating cost of $9. Which TV should the Gordons buy if they plan to keep it for 8 years? Use rational functions to help justify your answer.

A medication is administered to a patient and the concentration of the medication in the bloodstream is monitored. At time (in hours since giving the medication) the concentration, in mg/L, is modeled by the graph of the rational function on the right. Approximately when does the medication reach half of its highest concentration in the patient’s bloodstream?