36 Chapter 1 Real Numbers and Algebraic Expressions Student Check 6 Solve each problem. a. Suppose $2000 is invested in a certificate of deposit, CD, account that earns 5% annual interest for 4 yr. The amount of money in the account after 4 yr is given by Amount = 2000(1.05)4. Simplify this expression to determine the amount of money in the account in 4 yr. b. The Singapore Flyer is the world’s largest Ferris wheel. The Ferris wheel is in the shape of a circle. The distance around a circle is called its circumference. The circumference of a circle is twice the product of π and the radius of the circle, where r is the radius of the circle. i. Write an equation that represents the circumference of the circle. ii. If the radius of the Singapore Flyer is 75 m, find its circumference. Use 3.14 for π. c. The number of bachelor’s degrees conferred in the Computer and Information Sciences (CIS) majors from 1970 to 2005 are shown in the table. The number of degrees conferred in this field can be approximated by the expression 0.3x4 - 18x3 + 308.4x2 + 273.3x + 1096.6, where x is the number of years after 1970. (Source: National Center for Education Statistics) i. Write an equation that can be used to approximate the number of CIS degrees conferred, where d is the number of degrees. ii. Use the equation to estimate the number of degrees conferred in 2010. Round the answer to the nearest integer. d. The basal metabolic rate (BMR) for men is 66 plus 6.23 times a person’s weight in pounds +12.7 times a person’s height in inches minus 6.8 times a person’s age in years. i. Write an equation that represents a man’s BMR, where w is the man’s weight (in pounds), h is the man’s height (in inches), and a is the man’s age. ii. If Todd is a 43-yr-old who weighs 250 lb and is 6 ft 4 in. tall, what is his BMR? Round to the nearest integer. Troubleshooting Common Errors Some of the common errors associated with numerical expressions and algebraic expressions are shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. a. Simplify 3(4)2. �������������������������������������� ���������������������������������������������������������������� Based on the order of operations, we must evaluate the exponent first and then multiply. 3(4)2 3(16) 48 Objective 7 ▶ Troubleshoot common errors. 3(4)2 122 144 Years after 1970 Degrees Conferred 0 2388 5 5652 10 15121 15 42337 20 25159 25 24506 30 44142 35 47480 3 12
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