The sonar of a navy cruiser detects

(1) A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $67. A season ski pass costs $350. The skier would have to rent skis with either pass for $25 per day. Using linear equations, explain the process to find how many ski days it would take the skier to make the season pass less expensive than daily passes.

(2) Ace Manufacturing has determined that the cost of labor for producing transmissions is dollars, while the cost of materials is dollars.

a) Write a polynomial that represents the total cost of materials and labor for producing transmissions.

b) Using the website https://www.desmos.com/calculator, graph the polynomial , using the settings 0 to 1000 (step 100) for the x-axis and 0 to 1,000,000 (step 100,000) for the y-axis. Do not use commas in any of the numbers. Share the graph by exporting and downloading the image. Include the graph as part of your solution.

c) Using the function and the graph, explain the process to find the total cost for producing 500 transmissions.

d) Verify the answer from the previous problem by finding the cost of labor and cost of materials for producing 500 transmissions.

(3) The area of a rectangle is modeled by the polynomial square units. The width of the rectangle is modeled by the polynomial units. Showing all work, write a polynomial that represents the length of the rectangle.

(4) In 2012, Hurricane Sandy struck the East Coast of the United States, killing 147 people and causing an estimated $75 billion dollars in damage. With a gale diameter of about 1,000 miles, it was the largest ever to form over the Atlantic Basin. The accompanying data represent the number of major hurricane strikes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010.

Decade,

Major Atlantic Basin Hurricanes

1921–1930, 1

17

1931–1940, 2

16

1941–1950, 3

29

1951–1960, 4

33

1961–1970, 5

27

1971–1980, 6

16

1981–1990, 7

16

1991–2000, 8

27

2001–2010, 9

33

The polynomial function models the number of major Atlantic Basin hurricanes from the time period given in the table above.

a) Using the website https://www.desmos.com/calculator, graph the polynomial using the settings 0 to 10 (step 1) for the x-axis and 0 to 40 (step 5) for the y-axis. Share the graph by exporting and downloading the image. Include the graph as part of your solution.

b) Using the model and showing all work, estimate the number of major Atlantic Basin hurricanes between 1961 and 1970. Does this overestimate or underestimate the actual data shown in the table? By how much?

c) Using the model and showing all work, predict the number of major Atlantic Basin hurricanes between 2011 and 2020. Is your result reasonable?

d) The graph shows periods of increasing and periods of decreasing. Based on the graph alone, around what year did the number of major Atlantic Basin hurricanes start to decrease? Explain. Around what year did the number of major Atlantic Basin hurricanes begin to increase again? Explain.

(5) A balloonist throws a sandbag downward at 24 feet per second from an altitude of 720 feet. Its height (in feet) above the ground after seconds is given by .

a) What is the height of the sandbag 2 seconds after it is thrown? Explain.

b) How long does it take for the sandbag to reach the ground? Explain.

(6) A drug injected into a patient and the concentration of the drug in the bloodstream is monitored. The drug’s concentration, , in milligrams per liter, after hours is modeled by .

a) Use the site https://www.desmos.com/calculator to draw the graph of this function. Once you type the function in the cell (upper left), click the wrench symbol in the upper right (graph settings) and make the -axis from 0 to 10 (step 1) and the -axis from 0 to 3 (step 1). Share the graph by exporting and downloading the image. Include the graph as part of your discussion.

b) Using the graph, explain what happens to the drug concentration in the bloodstream over time.

c) Explaining the process, find the drug’s concentration after 3 hours.

d) What is the highest concentration of the drug in the bloodstream and when does it take place? Explain.

(7) The sonar of a Navy cruiser detects a submarine that is 2500 feet away. The point on the water directly above the submarine is 1500 feet away from the cruiser. What is the depth of the submarine? Explain.

(8) The polynomial function models a man’s normal systolic blood pressure, , at age . Showing all work, find the age, to the nearest year, of a man whose normal blood pressure is 125 mm Hg. Explain why one of the solutions is not relevant.