Name Date Class , 100, 1000, 10,000, common ratio:

Transcription

1 Name Date Class 11-1 Practice A Geometric Sequences Find the common ratio of each geometric sequence. Then find the next three terms in each geometric sequence. 1. 1, 4, 16, 64, 2. 10, 100, 1000, 10,000, common ratio: , 64, 32, 16, common ratio: common ratio: 4. 4, 20, 100, 500, common ratio: 5. The first term of a geometric sequence is 2 and the common ratio is 4. Find the 6th term. 6. The first term of a geometric sequence is 3 and the common ratio is 2. Find the 8th term. 7. The first term of a geometric sequence is 7 and the common ratio is 2. Find the 9th term. 8. What is the 5th term of the geometric sequence 9, 27, 81, 243,? common ratio (r): first term (a 1 ): 5th term: 9. What is the 13th term of the geometric sequence 2, 4, 8, 16,? common ratio (r): first term (a 1 ): 13th term: 10. Martin got a job at a starting pay of $8.00 per hour. His boss told him that if he works hard he can get a raise each year. The table shows Martin s wage for the first few years. Find Martin s hourly wage after 6 years. Round to the nearest cent. common ratio (r): first term (a 1 ): 6th term: Year Hourly Wage ($) 1 $ $ $ Holt McDougal Algebra 1

2 Name Date Class 11-1 Practice B Geometric Sequences Find the next three terms in each geometric sequence. 1. 5, 10, 20, 40, 2. 7, 56, 448, , 40, 160, 640, 4. 40, 10, 5 2, 5 8, 5. The first term of a geometric sequence is 6 and the common ratio is 8. Find the 7th term. 6. The first term of a geometric sequence is 3 and the common ratio is 1. Find the 6th term The first term of a geometric sequence is 0.25 and the common ratio is 3. Find the 10th term. 8. What is the 12th term of the geometric sequence 4, 12, 36,? 9. What is the 10th term of the geometric sequence 2, 6, 18,? 10. What is the 6th term of the geometric sequence 50, 10, 2,? 11. A shoe store is discounting shoes each month. A pair of shoes cost $80. The table shows the discount prices for several months. Find the cost of the shoes after 8 months. Round your answer to the nearest cent. Month Price 1 $ $ $ Holt McDougal Algebra 1

3 Name Date Class 11-2 Practice A Exponential Functions 1. If a superball is bounced from a height of 20 feet, the function f(x) = 20 (0.9) x gives the height of the ball in feet of each bounce, where x is the bounce number. What will be the height of the 6th bounce? Round your answer to the nearest tenth of a foot. Tell whether each set of ordered pairs satisfies an exponential function. Explain your answer. 2. {(1,10), (2, 20), (3, 40), (4, 80)} 3. {(1,5), (2, 10), (3, 15), (4, 20)} Graph each exponential function. 4. y = 2(3) x x y = 2 (3) x y (x, y) 2 y = 2(3) 2 1 y = 2(3) 1 0 y = 2(3) 0 1 y = 2(3) 1 2 y = 2(3) 2 5. y = 2(4) x x y = 2 (4) x y (x, y) In the absence of predators, the natural growth rate of rabbits is 4% per year. A population begins with 100 rabbits. The function f(x) = 100(1.04) x gives the population of rabbits in x years. 6. How long will it take the population of rabbits to double? 7. How long will it take the population of rabbits to reach 1000? Holt McDougal Algebra 1

4 Name Date Class 11-2 Practice B Exponential Functions 1. If a basketball is bounced from a height of 15 feet, the function f(x) = 15 (0.75) x gives the height of the ball in feet of each bounce, where x is the bounce number. What will be the height of the 5th bounce? Round to the nearest tenth of a foot. Tell whether each set of ordered pairs satisfies an exponential function. Explain your answer. 2. {(2, 4), (4, 8), (6, 16), (8, 32)} 3. {( 2, 5), ( 1, 10), (0, 15), (1, 20)} 4. {(1, 750), (2, 150), (3, 30), (4, 6)} 5. 5, 1 3, (0,1), (5, 3), (10, 9 ) Graph each exponential function. 6. y = 5(2) x 7. y = 2(3) x 8. y = x In the year 2000, the population of Virginia was about 7,400,000. Between the years 2000 and 2004, the population in Virginia grew at a rate of 5.4%. At this growth rate, the function f(x) = 7,400,000 (1.054) x gives the population x years after In what year will the population reach 15,000,000? 10. In what year will the population reach 20,000,000? Holt McDougal Algebra 1

5 Name Date Class 11-3 Practice A Exponential Growth and Decay Write an exponential growth function to model each situation. Then find the value of the function after the given amount of time. 1. Annual sales for a clothing store are $270,000 and are increasing at a rate of 7% per year; 3 years 2. The population of a school is 2200 and is increasing at a rate of 2%; 6 years y = ( 1+ ) y = y = ( 1+ ) y 3. The value of an antique vase is $200 and is increasing at a rate of 8%; 12 years y = y Write a compound interest function to model each situation. ( )( ) Then find the balance after the given number of years. A = $20,000 invested at a rate of 3% compounded annually; 8 years A 5. $35,000 invested at a rate of 6% compounded monthly; 10 years A = 1+ ( )( A 6. $35,000 invested at a rate of 8% compounded quarterly; 5 years A = A Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. 7. The population of a school is 800 and is decreasing at a rate of 2% per year; 4 years 8. The bird population in a forest is about 2300 and decreasing at a rate of 4% per year; 10 years y = ( 1 ) y y = ( 1 ) y 9. The half-life of strontium-90 is approximately 28 years. Find the amount of strontium-90 left from a 10 gram sample after 56 years. A = (0.5) A Holt McDougal Algebra 1

6 Name Date Class 11-3 Practice B Exponential Growth and Decay Write an exponential growth function to model each situation. Then find the value of the function after the given amount of time. 1. Annual sales for a fast food restaurant are $650,000 and are increasing at a rate of 4% per year; 5 years 2. The population of a school is 800 students and is increasing at a rate of 2% per year; 6 years 3. During a certain period of time, about 70 northern sea otters had an annual growth rate of 18%; 4 years Write a compound interest function to model each situation. Then find the balance after the given number of years. 4. $50,000 invested at a rate of 3% compounded monthly; 6 years 5. $43,000 invested at a rate of 5% compounded annually; 3 years 6. $65,000 invested at a rate of 6% compounded quarterly; 12 years Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. 7. The population of a town is 2500 and is decreasing at a rate of 3% per year; 5 years 8. The value of a company s equipment is $25,000 and decreases at a rate of 15% per year; 8 years 9. The half-life of Iodine-131 is approximately 8 days. Find the amount of Iodine-131 left from a 35 gram sample after 32 days Holt McDougal Algebra 1

7 Name Date Class 11-4 Practice A Linear, Quadratic, and Exponential Models Graph each data set. Write linear, quadratic, or exponential. 1. {(0, 4), (1, 2), (2, 0), (3, 2), (4, 4)} 2. {( 2, 5), ( 1, 8), (0, 9), (1, 8), (2, 5)} Look for a pattern in each data set. Write linear, quadratic, or exponential. 3. x y 4. x y 5. x y The data in the table show the price of apples at a local store over several years. Year Cost ($) a. Which model best describes the data for apples? b. Write the function that models the data for apples. c. Predict the cost of apples in year The data in the table show the price of a game over several years. Year Cost ($) a. Which model best describes the data for the game? b. Write the function that models the data for the game. c. Predict the cost of the game in year 7. Round the cost to the nearest cent Holt McDougal Algebra 1

8 Name Date Class 11-4 Practice B Linear, Quadratic, and Exponential Models Graph each data set. Which kind of model best describes the data? 1. {( 2, 0), ( 1, 3), (0, 4), (1, 3), (2, 0)} 2. {(0, 3), (1, 6), (2, 12), (3, 24), (4, 48)} Look for a pattern in each data set to determine which kind of model best describes the data. 3. {( 5, 9), ( 4, 0), ( 3, 7), ( 2, 12)} 4. {( 2, 9), ( 1, 13), (0, 17), (1, 21)} 5. {(1, 4), (2, 6), (3, 9), (4, 13.5)} 6. {(0, 4), (2, 12), (4, 36), (6, 76)} 7. (1,17), 3,8 1 2, 5,41 4, 7, Use the data in the table to describe how the restaurant s sales are changing. Then write a function that models the data. Use your function to predict the amount of sales after 8 years. 9. Use the data in the table to describe how the clothing store s sales are changing. Then write a function that models the data. Use your function to predict the amount of sales after 10 years. Restaurant Year Sales ($) 20,000 19,000 18,050 17, Clothing Store Year Sales ($) 15,000 15,750 16,500 17, Holt McDougal Algebra 1

9 Name Date Class 11-5 Practice A Square-Root Functions The function y = 12 x gives the total amount of framing needed, in feet, for a four-pane square window if x is the area of one window pane. 1. Find the amount of framing needed if the area of one window pane is 9 square feet. 2. Find the amount of framing needed if the area of one window pane is 5 square feet. Round your answer to the nearest tenth. Find the domain of each square-root function. 3. y = x 7 4. y = 4x y = x + 4 x 7 0 4x x x x 6. y = x 7. y = 4 5 x 8. y = 10 6x 12 3 Complete each function table. Then, graph each square-root function. 9. f(x) = x f(x) = 2x 11. f(x) = 2 x 1 x f(x) x f(x) x f(x) = 0 = = 1 = Holt McDougal Algebra 1

10 Name Date Class 11-5 Practice B Square-Root Functions 1. An apartment manager needs to order wallpaper border for the remodeled bathrooms. The function y = 640 x gives the amount of border needed, in feet, if x is the square footage of each bathroom. Find the amount of border needed if each bathroom is 100 ft The current I, in amps, flowing through a household appliance P is given by I =, where P is the power required in watts and R R is the resistance in ohms. What is the current in an electric skillet when the power required is 1500 watts and the resistance is 75 ohms? Round your answer to the nearest tenth. Find the domain of each square-root function. 3. y = x y = 3x 5. y = 2x + 8 x 6. y = 2 x 6 7. y = x 8. y = 7(x 3) 3 Complete each function table. Then graph each square-root function. 9. f(x) = 4x 10. f(x) = x f(x) = 1 2 x 2 x f(x) x f(x) x f(x) Holt McDougal Algebra 1

11 Name Date Class 11-6 Practice A Radical Expressions Complete the steps to simplify each expression = = = = = + = = 4. ( b 4) 2 = = 6. x 2 + 6x + 9 = Simplify. All variables represent nonnegative numbers = = b 2 c 2 = b 2 c 2 = 36 2 = 100 = = 2 = = = = xy = y 2 16x 4 = 9y x 4 21b 2 25c 4 = = = = 16. x 3 y x 4 100x b 3 16b x x A ladder is propped up against a house. The top of the ladder rests 18 ft above the ground and the base of the ladder is 4 ft from the building. Write the length of the ladder as a radical expression in simplest form. Then estimate the length to the nearest hundredth of a foot Holt McDougal Algebra 1

12 Name Date Class 11-6 Practice B Radical Expressions Simplify each expression = = = = 4. ( x + 8) 2 = = 6. x 2 + 8x + 16 = Simplify. All variables represent nonnegative numbers x 4 y x 4 y b 2 27b m 3 121n b 4 2b y 6 36y m 3 10n x q 10 5q Two hikers leave a ranger station at noon. Tom heads due south at 5 mi/h and Kyle heads due east at 3 mi/h. How far apart are the hikers at 4 PM? Give your answer as a radical expression in simplest form. Then estimate the distance to the nearest tenth of a mile Holt McDougal Algebra 1

13 Name Date Class 11-7 Add or subtract. Practice A Adding and Subtracting Radical Expressions = = m + 10 m = = = 6. b + 6 2b 5 b = Simplify each expression i i 2 i 3 + i 3 i 5 + i 25 i i 2 i 3 + i 3 i 5 + i i 2 + i 2 i 3 + i 3 i 5 + i i 2 i 3 i x + 16x x + 192x t + 243t + 3 3t 22. Find the perimeter of an equilateral triangle whose sides each measure 7 m inches. Give your answer as a radical expression in simplest form. 23. Find the perimeter of the rectangle shown at right. Give your answer as a radical expression in simplest form Holt McDougal Algebra 1

14 Name Date Class 11-7 Add or subtract. Practice B Adding and Subtracting Radical Expressions = = y + 6 y = b b = = x 4 2 = Simplify each expression x + 63x b + 27b m + 6 3m 4 2m m + 72m z + 2 8z 3 z t + 96t x + 117x k Write the numbers 3 8, 4 2and 50 in order from least to greatest. 26. The map at right shows the path traveled by a delivery person on his afternoon route. Write the total distance traveled as a simplified radical expression Holt McDougal Algebra 1

15 Name Date Class 11-8 Practice A Multiplying and Dividing Radical Expressions Multiply. Write each product in simplest form. ( ) i t i 40t 3i i i (5) t (40) t 45 2 i i 7 i 7 3i 200t i 5 i 7i7 3 i 2 i i i x i 8x i ( ) 2 ( ) ( ) t (2) ( ) ( ) ( t ) t ( 2 5)( 7+ 5) ( ) ( + ) ( 3+ 2)( 2 4) Simplify each quotient b 3 5 i i 3 5 i 2 b i ( 4+ 3)( 5 3) Holt McDougal Algebra 1

16 Name Date Class 11-8 Practice B Multiplying and Dividing Radical Expressions Multiply. Write each product in simplest form. 15 i 6 ( ) i x i 20x 3 6 i i (7 x)(20 x) i 5 5. ( ) b i 10b y y 8. 8( 12 2) 9. 2x ( 5 + 2x ) ( 7 5) ( 5m 4 ) 12. ( 4+ 3)( 2 3) ( 8 6) ( 2 + 8) 15. ( 5+ 2)( 6 2) ( 2 6) 17. ( 3 2)( 5+ 2) 18. ( 7+ 3)( 7 3) Simplify each quotient t z a 26. 8x 5 75k k Holt McDougal Algebra 1

17 Name Date Class 11-9 Practice A Solving Radical Equations Solve each equation. Check your answer. 1. x = x = 6 3. () x = (9) 2 ( 2x) = (6) 2 x = 2x = x = 2x 3 = 5 2x = ( 2x) 2 = ( ) 2 2x = x = 4. 4 x = x 2 4 = x = 3 x = x 2 = 3 2x + 1 = 7. 5 x = x = x = x + 3 = 3x 11. 4x + 1 = 5x x = 0 Solve each equation. Check your answer to determine whether any solution is extraneous. 13. x 4 = x 2 Check: ( ) 2 (x 4) 2 = x 2 x 2 8x + 16 = x 2 x 2 9x + 18 = 0 x = or x = x 4 = x 2 x 4 = x 2 The only solution is. 14. x 12 = 16x 15. 4x + 12 = The area of a triangle is 15 m 2. The height is 6 m, and the length of the base is 3x 5 m. What is the value of x? Holt McDougal Algebra 1

18 Name Date Class 11-9 Practice B Solving Radical Equations Solve each equation. Check your answer. 1. x = x 3. () x 2 3 = 5 = (11) 2 x = 15 x = x = 3x + 5 = 11 3x = 3x = x = 4. 2 x = x 2 = x = 6 7. x + 5 = 9 8. x 4 = x 4 = x 4 = x = x = x = x x + 2 = 2x x + 10 x + 13 = x = x x = 5 x x = x x = x = 2x According to Heron s formula, the area of a triangle is given by A = s(s a)(s b)(s c), where s is equal to one half its perimeter, and a, b, and c are the lengths of its sides. If a triangle has area 20 m 2, s = 10 m, a = 5 m and b = 2 m, what is c? Holt McDougal Algebra 1