MATH 121 Review Problems

MATH 121 Review Problems January 27/28

1. Suppose that your monthly cell phone bill is $50 when you use 1000 minutes and it is $65 when you use 1500 minutes. Find a linear relationship for your monthly cell phone bill as a function of minutes used. What are the units for the slope and what does it represent? What are the units for the y-intercept and what does it represent?

2. The population density in the U.S. has been growing approximately linearly. Let t = 0 represent the year 2000. The population density at t = 2 was 80 people per square mile and at t = 10, it was 86.7 people per square mile. Find a linear relationship for the population density as a function of t.

3. The risk of cardiovascular disease (CVD) for a person is approximately linearly related to the daily number of cigarettes smoked by that person. A person who smokes 10 cigarettes daily has a 0.8 percent chance of getting CVD. A person who smokes 30 cigarettes daily has a 1.0 percent chance of getting CVD. Find a linear relationship for the percent chance of CVD as a function of the daily number of cigarettes smoked.

4. In a sample of grasshopper mice in Kansas, one female's body was 100 mm long and she had 2 offspring. A second female's body was 110 mm long and she had 3 offspring. a) Find a linear relationship for the number of offspring as a function of the female's length. b) What are the units for the slope, and what does it represent? c) What are the units for the y-intercept and what does it represent? Is the y-intercept meaningful for this problem? Why?

5. The relationship between the weight, in kilograms, and the height, in centimeters, of young girls up to 36 months old is approximately linear. A typical 60 cm girl weighs 5 kg and a typical 100 cm girl weighs 15 kg. a) Find a linear relationship for the weight of a girl as a function of her length. b) What are the units for the slope and what does it represent? Be specific. c) What are the units for the y-intercept and what does it represent? Is the y-intercept meaningful for this problem? Why?

6. The U.S. infant mortality rate for African Americans is y = –0.41x + 22 and the U.S. infant mortality rate for whites is y = –0.18x + 10, where x is years since 1980. In what year will the two infant mortality rates be the same?

7. A 25-year old driver can see a road sign at about 500 feet and a 65-year old driver can see a road sign at about 400 feet. a) Find a formula for the distance at which a driver can see a road sign as a function of the driver's age. b) What are the units for the slope, and what does it represent? c) What are the units for the y-intercept and what does it represent? Is the y-intercept meaningful for this problem? Why?

8. Suppose that the fixed costs for making eyeglass lenses are $500 and that the total cost, including both fixed and variable costs, for producing 20 lenses is $1200. Find the total cost function for producing x lenses. 9. Suppose that the fixed costs for repairing tooth cavities are $200 and that the total cost, including both fixed and variable costs, for repairing 5 cavities is $375. Find the total cost function for repairing x cavities.

10. Suppose that a publisher's fixed costs are $2000 and the marginal cost for printing each book is $30. a) Write the total cost function for printing x books. b) If the books can be sold for $50 each, what is the total revenue for selling x books. c) What is the profit function? d) Use algebra to find the break even point.

11. Suppose that a potter's fixed costs are $200 and the marginal cost for creating each pot is $10. a) Write the total cost function for creating x pots. b) If the books can be sold for $25 each, what is the total revenue for selling x pots. c) What is the profit function? d) Use algebra to find the break even point.

12. For 28 female crustaceans, Platorchestia platensis, on Long Island their weights (x), in grams, and the number of eggs each carried (y) were recorded. The least squares line for these data are y = 1.61 x + 12.69 with R2 = 0.2054. a) What does the value of R2 tell you about the relationship between x and y? b) What are the units for the slope and what does it represent? Be specific. c) What are the units for the y-intercept and what does it represent? Is the y-intercept meaningful for this problem? Why?

13. An individual measured his heartrate, in beats per minute (bpm), while exercising on an elliptical machine at various speeds, in kilometer per hour (kph). The least squares line for these data are y = 3.75 x + 63.36 with R2 = 0.9763. a) What does the value of R2 tell you about the relationship between x Speed, x Heartrate, y and y? (kph) (bpm) 0 57 b) What are the units for the slope and what does it represent? Be 1.6 69 specific. 3.1 78 4 80 5 85 6 87 6.9 90 7.7 92 8.7 97 12.4 108 15.3 119

c) What are the units for the y-intercept and what does it represent? Is the y-intercept meaningful for this problem? Why?