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                                Algebraic Applications

 

1.Julie and some friends decided to take a trip around the Grand Canyon in Arizona and they traveled one-third of the distance by mule, 6 kilometers by boat, and one-half the distance by foot. How long was the trip.

 

2. Tim and Dustin are doing some community service. They are helping some of the elderly people in the neighborhood. If Tim can trim bushes in Ed’s yard in 5 hours, and Dustin could do the same job in 7 hours, how long would it take them working together to trim the bushes?

 

3. A student in algebra class needs 80% of all points on the tests to get a B. There are five 100 point tests and a 250 point final. The student’s test scores are 95, 87, 64, 72, and 81. What is the least score he can make on the final and still get a B?

 

4. On Saneomi’s trip to San Francisco he rented a car. The charge was $21 per day and 10 cents per mile. If he rented the car for 2 days, how far was it driven if the total bill came to $53.20?

 

5. Kaianoa talked to his brother in Honolulu the other day, and he said that the temperature was ranging between 77 and 86 degrees Fahrenheit. What is that range in degrees Celsius? (F=9/5 C+32)

 

6. Since the weather has been so good recently, Greg and his wife decided to go to the Clackamas River and rent a motorboat. They got there at 7 am and only had enough money to rent the boat for five hours. They were told that the boat would travel at 8 kilometers per hour upstream and 12 kilometers per hour returning. They wanted to go as far up the river as possible and still be back by noon. At what time would they need to turn back, and how far from the resort will they be at that time?

 

7. A car traveling at a speed of v miles per hour, the least number of feet d under the best possible conditions that is necessary to stop a car (including a reaction time) is given by the empirical formula d = 0.044v^2 + 1.1v. Estimate the speed of a car requiring 165 feet to stop after danger is realized.

 

8. Taro discovered one night that the area of a particular triangle is 2 ft^2, and its base is 3 feet longer than its height. What is the height and base of the triangle? (The formula for the area of a triangle is A = ½bh.)

 

9. Use the formula A = P(1 + r)2 to find the rate of interest necessary for $10,000 to grow to $12,321 in two years, if the interest is compounded annually.

 

10. As Concordia was planning the new Library, it was decided that we wanted a rectangular field that is twice as long as it is wide for the lawn in front of the building. Find the actual dimensions of the field if it has a total area of 5000 sq. yards.

 

                         GRAPHING APPLICATIONS

 

11. In 1948 Professor Brown, a psychologist, trained a group of rats (in an experiment on motivation) to run down a narrow passage in a cage to receive food in a box. A harness was put on each rat and the harness was then connected to an overhead wire that was attached to a scale. In this way the rat could be placed at different distances (in centimeters) from the food and Professor Brown could then measure the pull (in grams) of the rat toward the food. It was found that a relation between motiation (pull) and position was given approximately by the equation p=-15d+70, 30 < d < 175.Graph this equation for the indicated values of d.

 

12. In biology there is an approximate rule, called the bioclimatic rule, for temperate climates. This rule states that in spring and early summer, periodic phenomena such as blossoming for a given species, appearance of certain insects, and ripening of fruit usually come about four days later for each 500 feet of altitude. Stated as a formula:

d = 4(h500)where d = change in days and h = change in altitude in feet. Graph the equation for 0< h < 4,000

 

13. If a certain amount of money, P called principal, is invested at 100r% interest

compounded annually, the amount of money A after t years is given by: A = P(1+r)t

Graph this equation for P = $10, r = .10 and 0t10, and explain in words what information you can learn from this graph.

14. The atmospheric pressure P, in pounds per square inch, can be calculated approximately using the formula: P = 14.7e-.21x where x is altitude relative to sea level in miles. Graph the equation for -1x5, and explain in words what information you can learn from this graph.

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