# Several Algebra Excercises

Please have a look to the attached word document with several algebra exercises.

Section 3.1

Exercise 92- Page 179

Solve each problem. See Example 8.

92. Dental services. The national cost C in billions of dollars for dental services can be modeled by the linear equation

where n is the number of years since 1990 (Health Care Financing Administration, www.hcfa.gov).

a) Find and interpret the C-intercept for the line.

b) Find and interpret the n-intercept for the line.

c) Graph the line for n ranging from 0 through 20.

d) If this trend continues, then in what year will the cost of dental services reach 100 billion?

Exercise 94- Page 179

Solve each problem. See Example 8.

94. Demand equation. Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is $5 per can. After experimenting with prices for some time, Helen has determined that the weekly demand can be found by using the equation

where d is the number of cans and p is the price per can.

a) Will Helen sell more or less Muscle Punch if she raises her price from $5?

b) What happens to her sales every time she raises her price by $1?

c) Graph the equation.

d) What is the maximum price that she can charge and still sell at least one can?

Section 3.2

Exercise 62- Page 193

Solve each problem. See Examples 8 and 9.

62. Retirement pay. The annual Social Security benefit of a retiree depends on the age at the time of retirement. The accompanying graph gives the annual benefit for persons retiring at ages 62 through 70 in the year 2005 or later (Social Security Administration, www.ssa.gov). What is the annual benefit for a person who retires at age 64? At what retirement age does a person receive an annual benefit of $11,600? Find the slope of each line segment on the graph,

and interpret your results. Why do people who postpone retirement until 70 years of age get the highest benefit?

Section 3.3

Exercise 90- Page 203

Solve each equation. See Example 7.

90. Marginal revenue. A defense attorney charges her client $4000 plus $120 per hour. The formula gives her revenue in dollars for n hours of work. What is her revenue for 100 hours of work? What is her revenue for 101 hours of work? By how much did the one extra hour of work increase the revenue? (The increase in revenue is called the marginal revenue for the 101st hour.)

Exercise 92- Page 203

Solve each equation. See Example 7.

92. Single women. The percentage of women in the 20-24 age group who have never married went from 55% in 1970 to 73% in 2000 (Census Bureau, www.census.gov). Let 1970 be year 0 and 2000 be year 30.

a) Find and interpret the slope of the line through the points (0, 55) and (30, 73).

b) Find the equation of the line in part (a).

c) What is the meaning of the y-intercept?

d) Use the equation to predict the percentage in 2010.

e) If this trend continues, then in what year will the percentage of women in the 20-24 age group who have never married reach 100%?

Section 3.4

Exercise 78- Page 212

Solve each problem. See Example 5.

78. Direct deposit. The percentage of workers receiving direct deposit of their paychecks went from 32% in 1994 to 60% in 2004 (www.directdeposit.com). Let 1994 be year 0 and 2004 be year 10.

a) Write the equation of the line through (0, 32) and (10, 60) to model the growth of direct deposit.

b) Use the graph on the next page to predict the year in which 100% of all workers will receive direct deposit of their paychecks.

c) Use the equation from part (a) to predict the year in which 100% of all workers will receive direct deposit.

Exercise 80- Page 213

Solve each problem. See Example 5.

80. Age at first marriage. The median age at first marriage for females increased from 24.5 years in 1995 to 25.1 years in 2000 (U.S. Census Bureau, www.census.gov). Let 1995 be

year 5 and 2000 be year 10.

a) Find the equation of the line through (5, 24.5) and (10, 25.1).

b) What do x and y represent in your equation?

c) Interpret the slope of this line.

d) In what year will the median age be 30.

e) Graph the equation.

Exercise 92- Page 215

Solve each problem. See Example 5.

92. Basal energy requirement. The basal energy requirement B is the number of calories that a person needs to maintain the life process. For a 28-year-old female with a height of 160 centimeters and a weight of 45 kilograms (kg), B is 1300 calories. If her weight increases to 50 kg, then B is 1365 calories. There is a linear equation that expresses B in terms of her weight w. Find the equation and find the basal energy requirement if her weight is 53.2 kg.

Section 3.5

Exercise 48- Page 222

Solve each problem.

48. Gas laws. The volume of a gas is inversely proportional to the pressure on the gas. If the volume is 6 cubic centimeters when the pressure on the gas is 8 kilograms per square centimeter, then what is the volume when the pressure is 12 kilograms per square centimeter?

Exercise 52- Page 223

Solve each problem.

52. Ideal waist size. According to Dr. Aaron R. Folsom of the University of Minnesota School of Public Health, your maximum ideal waist size is directly proportional to your hip size. For a woman with 40-inch hips, the maximum ideal waist size is 32 inches. What is the maximum ideal waist size for a woman with 35-inch hips?

Section 3.6

Exercise 14- Page 229

Graph each inequality. See Examples 2 and 3.

Exercise 24- Page 230

Graph each inequality. See Examples 2 and 3.

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#### Solution Summary

Detailed step by step solution is provided to all the problems. Graphs are also provided.