College Algebra. Word Problems

Transcription

1 College Algebra Word Problems

2 Example 2 (Section P6) The table shows the numbers N (in millions) of subscribers to a cellular telecommunication service in the United States from 2001 through 2010, where t represents the year. Sketch a scatter plot of the data.

3 Example (Section P.6.) The following chart represents the grain output (in million bushels) of a certain state during the 1990s. Year Output Let x = 0 represent the year Draw a scatter plot of the data. Be sure and label the horizontal and vertical axis.

4 Example 6 Female Participants in Athletic Programs (Section 1.2.) The number y (in millions) of female participants in high school athletic programs in the United States from 2000 through 2010 can be approximated by the linear model y = 0.045t , 0 t 10 where t = 0 represents 2000.

5 Example 6 Female Participants in Athletic Programs cont d (a) Find algebraically and interpret the y-intercept of the graph of the linear model shown in Figure (b) Use the linear model to predict the year in which there will be 3.42 million female participants. Female Participants in High School Athletics Figure 1.10

6 Checkpoint (Section 1.2.) The numbers y ( in millions) of male participants in high school athletic programs in the United States from 2000 through 2010 can be approximated by the linear model y = 0.064t , 0 t 10 Where t = 0 represents (a) Find algebraically and interpret the y-intercept of the graph of the linear model. (b) Use the linear model to predict the year in which there will be 4.79 million male participants.

7 Example (section 1.2.) For a local delivery company with a fleet of vans, the annual operating cost, C, per van and the number of miles traveled, x, by a van in a year are related linearly by the equation C = x A. Find the cost to operate a van that travels 10,000 miles in a year. B. Find the number of miles that will yield an annual operating cost of $5,000.

8 Example 9 (Quadratic Modeling: Internet Users) (Section 1.4) From 2000 through 2010, the numbers of Internet users I ( in millions ) in the United States can be approximated by the quadratic equation I = 0.898t t , 0 t 10 Where t represents the year, with t = 0 corresponding to According to the model, in which year did the number of Internet users reach 200 million?

9 Example 5 (Section 2.1.) The maximum recommended slope of a wheelchair ramp is 1/12. A business is installing a wheelchair ramp that rises 22 inches over a horizontal length of 24 feet. Is the ramp steeper than recommended?

10 Example 6 (Section 2.1.) A kitchen appliance manufacturing company determines that the total cost C ( in dollars ) of producing x units of a blender is C = 25x Describe the practical significance of the y-intercept and slope of this line.

11 Example 7 (Section 2.1.) A college purchased exercise equipment worth $12,000 for the new campus fitness center. The equipment has a useful life of 8 years. The salvage value at the end of 8 years is $2000. Write a linear equation that describes the book value of the equipment each year.

12 Example 8 (Section 2.1.) The sales for Best Buy were approximately $49.7 billion in 2009 and $50.3 billion in Using only this information, write a linear equation that gives the sales in terms of the year. Then, predict the sales in 2013.

13 Example 9 (Section 2.2.) A batter hits a baseball at a point 3 feet above ground at a velocity of 100 feet per second and an angle of 45. The path of the baseball is given by the function f x = x 2 + x + 3 Where f(x) is the height of the baseball ( in feet ) and x is the horizontal distance from home plate ( in feet ). Will the baseball clear a 10-foot fence located 300 feet from home plate?

14 Example 7 (Section 2.3.) The distance s ( in feet ) a moving car is from a stoplight is given by the function s t = 20t 3/2 Where t is the time ( in seconds). Find the average speed of the car (a) From t 1 = 0 to t 2 = 4 seconds and (b) From t 1 = 4 to t 2 = 9 seconds.

15 Example 5 (Section 3.1.) The path of a baseball after being hit is given by the function f x = x 2 + x + 3, where f(x) is the height of the baseball( in feet) and x is the horizontal distance from home plate (in feet). What is the maximum height of the baseball?

16 Exercise 3.1. p249 #77 A manufacturer of lighting fixtures has daily production costs of C = x x 2, where C is the total cost ( in dollars ) and x is the number of units produced. How many fixtures should b produced each day to yield a minimum cost?

17 Exercise 3.1. p249 #79 The total revenue R earned ( in thousands of dollars ) from manufacturing handheld video games is given by R p = 25p p Where p is the price per unit ( in dollars). (a) Find the revenues when the prices per unit are $20, $25, and $30. (b) Find the unit price that will yield a maximum revenue, What is the maximum revenue? Explain your results.

18 Example 8 (section 5.1) You invest $12,000 at an annual rate of 3%. Find the balance after 5 years when the interest is compounded a. Quarterly b. Monthly c. continuously

19 Example 9 (section 5.1) In 1986, a nuclear accident occurred in Chernobyl in what was then the Soviet Union. The explosion spread highly toxic radioactive chemicals, such as plutonium, over hundreds of square miles, and the government evacuated the city and the surrounding area. To see why the city is now uninhabited, t/24,100 consider the model P = Which represents the amount of plutonium P that remains ( from the initial amount of 10 pounds) after t years. a. Sketch the graph of this function over the interval from t=0 to t=100,000, where t=0 represents b. How much of the 10 pounds will remain in the year 2017? c. How much of the 10 pounds will remain after 100,000years?

20 Example 11 (Section 5.2.) Students participating in a psychology experiment attended several lectures on a subject and took an exam. Every month for a year after the exam, the students took a retest to see how much of the material they remembered. The average scores for the group are given by the human memory model f t = 75 6 ln t + 1, 0 t 12, where t is the time in months. a. What was the average score on the original exam (t=0)? b. What was the average score at the end of t=2 months? c. What was the average score at the end of t=6 months?

21 Example 10 (Section 5.4.) You invest $500 at an annual interest rate of 6.75%, compounded continuously. How long will it take your money to double?

22 Example 11 Section 5.4. The retail sales y ( in billions of dollars ) of e-commerce companies in the United States from 2002 through 2010 can be modeled by y = ln t, 12 t 20 Where t represents the year, with t = 12 corresponding to During which year did the sales reach $141 billion?

23 Example 1 Section 5.5. An exponential growth model that approximates the data which estimates the amounts in billions of dollars of U.S. online advertising spending from 2011 through 2015 is given by S = 9.30e t, 11 t 15 where S is the amount of spending in billions of dollars and t=11 represents According to this model, when will the amount of U.S. online advertising spending reach $80 billion?

24 Example 2 Section 5.5. In a research experiment, a population of fruit flies is increasing according to the law of exponential growth. After 2 days there are 100 flies, and after 4 days there are 300 flies. How many flies will there be after 5 days?

25 Example The rate of population growth for a certain city is 3% per year. Find the number of years necessary for the present population of 100,000 people to double.

26 Example 8 Section 6.2 An airplane flying into a headwind travels the 2000mile flying distance between Chicopee, Massachusetts, and Salt Lake City, Utah, in 4 hours and 24 minutes. On the return flight, the airplane travels this distance in 4 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

27 Example 9 Section 6.2. The demand and supply equations for a video game console are p = x p = x where p is the price per unit in dollars and x is the number of units. Find the equilibrium point for this market. The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.