Back to Lesson 7-1 7-1B VOCABULARY 1. Arturo deposits $3,000 into a savings account. At the end of the year, the bank pays him 4% interest, which amounts to $120. The total amount of money in his account is now $3,120. The net year, the bank will pay him 4% interest on $3,120, assuming he makes no deposits or withdrawals. a. Is the interest in the second year simple or compound interest? Why or why not? b. What is the principal in this situation? c. What is the annual yield? d. What is the total interest paid to Arturo at the end of the second year? 2. the following for the epression 3 5. a. base b. power c. eponent d. coefficient USES Objective D 3. a. Write an epression that you could use to find the amount in an account if $10,000 is invested at 6% annual yield for 10 years. b. Write an epression that you could use to find the amount in an account if P dollars is invested at 6% annual yield for t years. Algebra 371
Back to Lesson 7-1 7-1B page 2 4. A bank uses the spreadsheet below to show the amount in a savings account earning 4.5% interest annually. The principal invested is $2,100. A B C 1 Year Balance Annual Interest 2 0 2,100.00 3 1 2,194.50 94.50 4 2 2,293.25 98.75 5 3 2,396.45 103.20 6 4 a. Multiple Choice. Which epression does the bank use to calculate the balance in the savings account? A 2,100(0.45) t B 2,100(0.045) t C 2,100(1.045) t D 2,100(1.45) t b. What number should appear in cell B6? c. What number should appear in cell C6? d. What trend do you notice in the Annual Interest column? 5. Most car-loan companies charge interest every month on your balance from the previous month. Suppose your balance is $15,720 and your monthly interest rate is 0.73%. How much interest will you pay that month? 6. Suppose Shawna deposited $400 in a savings account that has an annual yield of 4.7%. a. How much money will Shawna have in her savings account at the end of 8 years? b. How much interest will Shawna have earned? 7. Which investment yields more? Eplain your answer. a. an amount invested for 5 years at an annual yield of 3%. b. the same amount invested for 2.5 years at an annual yield of 6%. 372 Algebra
Back to Lesson 7-2 7-2A USES Objective D In 1 3, match the scenario to the correct formula listed below. A P = 7(1.02) t B P = 7(2) t C P = 7(1.2) t 1. A colony of bacteria doubles every hour. If a scientist started with 7 cells, how many cells would there be in t hours? 2. Scientists introduced 7 sea turtles into the ocean. They hope the sea turtle population grows by 2% each year. How many sea turtles will there be in t years? 3. When Pricy Pants Company opens a new store, they charge $7 for a pair of pants. Each year their cost of pants increases by 20%. How much will it cost to buy a pair of pants t years from the opening year? 4. Anya has started a new job paying $8.00 per hour. Assuming that her work is ecellent, she will get a 5% raise every 4 months. a. After 3 years, how many raises will she have gotten? b. What will her pay rate be after 3 years? c. If her employer kept giving her pay raises this way, what would her pay rate be after she had been working for 10 years? REPRESENTATIONS Objective H 5. The president of Acme Industries predicts that the sales of a new product will grow by 35% every year for the net 5 years. This year s sales were $40,000. a. Make a table of values showing the b. Graph the sales for the first five years. amount of sales 0, 1, 2, 3, 4 and 5 years from now. Algebra 373
Back to Lesson 7-3 7-3A USES Objective E 1. In 2006, a particular car cost $21,725. Suppose its value depreciates 8% each year. a. What will the value of the car be in 2007? b. Write a formula that gives the value of the car t years from when it was purchased. c. How much will the 2006 car be worth in 2012? d. In what year will the 2006 car be worth less than $10,000? 2. Multiple Choice. Which equation represents a starting amount depreciating at a rate of 13% each year? A y = b(1.13) t B y = b(0.13) t C y = b(0.87) t D y = b(1.87) t 3. Write an equation in the form y = b g to describe the numbers in the calculator display at the right. REPRESENTATIONS Objectives G and H 4. A biologist is studying how a new medicine affects the number of antibodies a patient has to fight disease. The number may grow at a constant rate or eponentially. The biologist looks at how 100 antibodies might increase in two cases. Case 1: There are 30 more each day. Case 2: There are 20% more each day. Let = the number of days. a. Write an epression for the number of antibodies if there are 30 added each day. b. Write an epression for the number of antibodies if they are increasing eponentially by 20% each day. c. Fill in the chart above. Round to the nearest integer. d. Which case gives more antibodies after 4 days? Day Increase by 30 Increase by 20% 0 100 100 1 2 3 4 5 6 7 8 9 10 e. Which gives more antibodies after 10 days? 376 Algebra
Back to Lesson 7-4 7-4A USES Objectives E and F In 1 5, multiple choice. Tell if the situation described is: A eponential growth C constant increase B eponential decay D constant decrease 1. Every year, there are 5% fewer patients with the disease. 2. With better techniques, farmers are able to increase their output 3% each year. 3. Each year, there are 30 fewer students in the school. 4. In a single-elimination tournament, half of the teams are eliminated in each round of play. 5. Every time Joan took the test her score increased points. 6. Amalgamated Industries receives hundreds of applications for each job opening. Their selection process is to review applications and discard 50% of them. This is repeated until only one applicant is left. Let n = the number of times that half the applications are discarded. a. Write an epression of the form b g n to describe the number of people left after the applications have been reviewed n times. b. If 512 people apply for a job, how many are left when n = 4? REPRESENTATIONS Objective H 7. It seems like there are coffee stores on every corner in some neighborhoods. At the right is a table that shows the total number of coffee stores each year since 1987. a. Create a scatterplot on your calculator. Does the data appear to be linear or eponential? b. Using regression, find an equation to fit the data. Let = the number of years since 1987. c. Use your equation from Part b to predict how many stores there will be in 2013. d. In what year will there be more than 20,000 stores? Year Number of Stores 1987 17 1988 33 1989 55 1990 84 1991 116 1992 165 1993 272 1994 425 1995 676 1996 1,015 1997 1,412 1998 1,886 1999 2,135 2000 3,501 2001 4,709 2002 5,886 2003 7,225 2004 8,337 Algebra 379
Back to Lesson 7-7 7-7A SKILLS Objective B 1. Steve has saved $150. He plans to save an additional $25 each month. To keep track of his savings, he wants to create a spreadsheet like the one at the right. a. What formula can Steve enter in cell B4 to find the amount of money he has saved after 2 months? b. Fill in the values in Column B. c. Eplain what the value in cell B7 represents. A 1 Month Money Saved 2 0 150 3 1 175 4 2 5 3 6 4 7 5 8 6 9 7 10 8 B USES Objective G In 2 5, multiple choice. Each graph at the right is drawn on the window 2 15 and 2 y 15. Match each equation with its graph. 2. f() = 2 + 7 3. g() = 4 0.5 A C B D 4. h() = 2 1.5 5. j() = 0.5-2 6. Minnie and Ma are twins. Currently their weekly allowance is $5.00. Minnie wants her allowance to increase by $3.00 each year. Ma wants his to increase by 30% each year. The twins present their allowance proposals to their parents using a spreadsheet like the one at the right. a. What formula can Minnie enter in B3 to display her allowance a year from now? b. What formula can Ma enter in C3 to display his allowance a year from now? c. Which twin will have a greater weekly allowance for the net three years? A B C 1 Year Minnie s Ma s 2 0 5 5 3 1 4 2 5 3 d. Which twin will have a greater weekly allowance si years from now? 388 Algebra
Back to Lesson 7-5 7-5B PROPERTIES Objective C 1. Suppose a function f consists only of the ordered pairs ( 2, 5), ( 1, 2), (5, 2), (6, 7), and (8, 25). a. What is the domain of f? b. What is the range of f? 2. Multiple Choice. Which list does not describe a function? A y B y C y D 1 2 0 2 1 3 1 2 1 3 0 1 1 0 0 0 1 1 y 1 2 0 3 1 4 REPRESENTATIONS Objective I 3. The graph below is of a function showing the dollars spent on clothes over a period of 6 months. 250 Total Money Spent on Clothes ($) 200 150 100 50 0 1 2 3 4 5 6 Month a. Find the value of the function when = 5. b. Find the value of the function when = 3.5. c. Find when the function is $50. d. Use inequalities to describe the domain and range of this function. Algebra 383
Back to Lesson 7-5 7-5B page 2 4. The graph of a function is shown at the right. 10 y a. From the graph, determine the domain of the function. 6 4 b. From the graph, determine the range of the function. 8 6 2 4 2 2 4 6 8 2 4 c. Give the range that corresponds to a domain of { : < 2}. 6 8 10 5. Consider the function described by y = 2-2. y a. Graph the function on the grid at the right. b. What is the domain of the function? c. What is the range of the function? 6. The function y = 2 1.5 is graphed at the right. y 12 a. True or False. 0 is in the range of this function. 10 8 6 4 b. What is the value of this function when = 0? 2 8 6 2 2 4 6 8 2 c. What is the domain of the function that is graphed? d. Suppose can be any negative integer or zero. What is the least possible value of y? 4 6 8 10 12 384 Algebra
Back to Lesson 7-6 7-6A PROPERTIES Objective C 1. Suppose a function f consists only of the ordered pairs (0, 1), (1, 3), (2, 9), (3, 27), and (4, 81). a. What is the domain of f? b. What is the range of f? c. Write a formula for f() in terms of. 2. Consider the function L described by the equation L() = 8-15. a. Find L(3). b. Find L( 2.5). c. True or False. L(6) < L(0.4) REPRESENTATIONS Objective I In 3 and 4, graph the function on the given domain. 3. f() = 2-6, 4 3 4. h() = 1 4 2, 0 6 f() h() 5. Use the graph of linear function G shown at the right. a. Find G( 6). b. Find G(1). c. True or False. G( 4) = 3. G() 8 6 4 2 8 6 4 2 4 6 8 2 d. Give a formula for G() in terms of. 6 8 Algebra 385