Study Guide With Answers

Evaluate the expression. 2. T1 3. -5 (-6) 3-2 5. -125 6. 128 ..!. 3 6 7 Simplify the expression. Write your answer using only positive exponents. 4. V-129 11. (x s ) Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. 9 17. y=0.75(1.05) 1 9 12. (x-5) 13. (3t)-4 14. ( 5! 5 4 r Evaluate the function for the given value of x. 15. y=Y;x=2 16. fix)=-4(4t; X = 2 19. You deposit $2800 in a savings account that earns 1 % annual interest compounded semiannually. Write a function that represents the balance after t years. Solve the equation. 20. 3 4x =3 40 5x 4 22. 100 - =10-x- l ID: A Name: 30 -2x+3 23 24 1 = JZ 163'*2 You want to determine how quickly messages can spread on a social media website' On the first day, you create a message that is sharecl with 2 people' On the second day, each ofthose people share it with 3 people. On third day, everyone who received the message shares it with 3 more people, and so on. Write an equation that represents the nth term of the geometric sequence. Then ftnd ar. You work for a design company and want to enlarge one ofyour designs for a new billboard sign. You can enlarge the design by I20Yo every time you run the program. The original design is 12 inches wide by 24 inches long' a. Write 9, l, -7, - 15, width after r times that you run the Program. b. How wide is the design after running the program five times? c. How many times will you have to run the program for the design to be at least 150 feet wide? Write a recursive rule for the sequence. 25. a function that reprcsents the -23,... 31. You buy a used car for $6599' Its value decreases by 12% every Year. Bvaluate the exPression. 26. 'J 64 a. Write a function that represents the value y (in dollars) ofthe car aftet t Years. 27. tlotl' b. What is the value of the car after 2'5 years? c. What is the value of the car after 20 years? 28. (Jr)' d. According will the value of the car be zero? $675 in a savings account that earns rnonthly' compounded interest 60lo 29. You deposit 32. a. Write a function that represents the balance after / years. b. What is the balance to the model, when The function f(t) -- 16(1.4)' represents the number of deer in a tbrest after t Years' a. Does the function represent exponential growth or exponential decaY? after 3 Years? b. Graph the function on a calculator' Describe the domain and range. c. What is the yearly percent change? d. What is the approximate monthly percent change? e. How many deer are in the forest after 6 years? 2 ID: A Name: 34. -80,40, -20,r0, Determine whether the sequence is ørithmetic' geomeftic, or neitltet. 33.1,3,6,r0, 35 The bacteria E. colioften a single E' cause illness among people who eat infected food. Suppose that coli bacterium in a batch of ground beef begins doubling every minute. a. cornplete the table below that represents the number of bacteria Minutes, x 0 I a 2 4 J after x minutes' (Assume no bacteria die') 6 5 Number of bacteria, V b. write in the food after any number of minutes' an equation that can be used to calculate the number of bacteria c. How many 36' bacteria will there be aftet 20 minutes? Determine whether the table represents a linear exponenlial function. Explain. or ^n The function P(r) = 2000(1'5)' represents the population of a smalltown. 37 a. Does the function represent exponential growth or exponential decaY? b. What is the yearly percent change in population? c. x v 0 J 1 7 2 11 J 15 x 1 v 2 2 4 What is the approximate monthly percent 38, change? d. How many people are living in the town after 3 years? J I 4 t6 Numeric Response 39 using its lowest magnification lens' A microscope allows a scientist to view bacteria at four times their actual size y in comparison to microscope, the size of the image increases. The size of the image with each lens added to the dby y = its original size after x magnification lenses are added is represente be added so the new image is 128 times the original size? J 4(2)'' How many more lenses should ID: A Name: Other 40 a musical piece. The table shows the durations (in fractions of a whole note) of each type of note played during Note quaúer half whole I I 1 2 1 23 22 sixteenth eighth 1 Duration 24 a. Compare the duration of eighth notes to the duration of sixteenth notes. b. How many half notes are in 15 whole notes? notes. There are 32 thirty-second notes in a whole note. How could you of 2? compare the duration of éach note to the duration of a thirty-second note? Can you still use a base c. Drummers often use thirty-second Explain. representing 41,. A coordinate plane can be used to map the routes of trade ships in the Atlantic Ocean with the x-axis the path of a second the Equator. The path of the first trade ship can be represented by function - 3-z'-t, while trade ship can be represented by the function = -5x -8' ! ! a. Graph the paths of the two ships in the same coordinate plane. b. Will the fwo trade ships cross paths? If so, approximate the x-value(s) of the coordinate(s). better choice needs transpofted to the southern part of the Atlantic Ocean, Which ship would be the to carry the shiPrnent? ExPlain. c. A shipment 4 ID: A Answer Section SHORT ANSWER 1. ANS: 1 DIF: PTS: 1 NAT: HSN-RN.A.2 NOT: Example 1 2. ANS: 1 7 Level 1 REF: Algebra 1 Sec. 6.1 KEY: zero exponents I evaluate DIF: PTS: 1 NAT: HSN-RN.A.2 NOT: Example 1 3. ANS: 1 864 Level I REF: Algebra 1 Sec. 6.1 KEY: negative exponents I evaluate PTS: 1 DIF: NAT: HSN-RN.A.2 NOT: Example I 4. ANS: -9 Level I REF: Algebra 1 Sec. 6.1 KEY: zero exponents I negative exponents I evaluate PTS: 1 DIF: Level I NAT: HSN-RN.A.1 I HSN-RN.A.2 NOT: Example 2 5. ANS: -5 REF: Algebra 1 Sec. 6.2 KEY: evaluate I nth root of a number I finding nth roots DIF: Level 1 PTS: 1 NAT: HSN-RN.A. I I HSN-RN.A.2 NOT: Example 2 6. ANS: 64 REF: Algebra 1 Sec. 6.2 KEY: evaluate I nth root of a number I finding nth roots - DIF: Level I PTS: 1 NAT: HSN-RN.A.I I HSN-RN.A.2 NOT: Example 3 REF: Algebra 1 Sec. 6.2 KEY: evaluate I evaluating expressions with rational exponents ID: A 7, ANS 4 r 8 DIF: Level PTS: 1 NAT: HSN-RN.A.2 I REF: Algebra 1 Sec.6'1 KEY: simplify I negative exponents I zero exponents REF: Algebra 1 Sec.6.1 KEY: simplify I negative exponents I zero exponents REF: Algebra 1 Sec.6.1 KEY: simplify I negative exponents I zero exponents NOT: Example 2 8. ANS: sto 6418 DIF: Level I PTS: 1 NAT: HSN-RN.A.2 NOT: Example 2 9. ANS: v 4 7226 DIF: Level PTS: 1 NAT: HSN-RN.A.2 1 NOT: Example 2 10, ANS: btl 1 DIF: Level I REF: Algebra 1 Sec.6.1 KEY: properties of exponents lsimplify DIF: Level I PTS: I NAT: HSN-RN.A.2 REF: Algebra 1 Sec.6.l KEY: properties of exponents lsimplify PTS: NAT: HSN-RN.A.2 NOT: ExamPle 3 1 1. ANS: )cot NOT: Example 3 12. ANS: 1 x 45 PTS: 1 NAT: HSN-RN.A.2 NOT: Example 3 DIF: Level 1 REF: Algebra 1 Sec.6.1 KEY: properties of exponents lsimplify 2 ID: A 13. ANS: I 8lt4 DIF: Level PTS: 1 NAT: HSN-RN.A.2 1 REF: Algebra 1 Sec. 6.1 KEY: properties of exponents I simplif NOT: Example 4 14. ANS: 625m20 t6 PTS: NAT: 1 DIF: HSN-RN.A.2 Level I REF: Algebra 1 Sec. 6.1 KEY: properties of exponents I simplify NOT: Example 4 15. ANS: 9 PTS: NAT: KEY: 16, REF: Algebra 1 Sec. 6'3 Level I HSF-IF.C.9 | HSF-BF.A.1a IHSF-LE.A'1a IHSF-LE.A.2 evaluating exponential functions I exponential function NOT: Exarnple 2 I DIF: ANS: -64 REF: Algebra 1 Sec' 6.3 DIF: Level 1 PTS: I NAT: HSF-IF,C.9 IHSF-BF.A.1a IHSF-LE'A'1a I HSF-LE.A.2 KEY: evaluating exponential functions I exponential function NOT: Example 2 17. ANS: exponential growth; 5% REF: Algebra I Sec. 6.4 DIF: Level I PTS: I HSF-BF.A.1a NAT: HSA-SSE.B.3c I HSF-IF,C.8b I I HSF-LE'A.1c KEY: identifying exponential growth ancl clecay functions I interpreting 18 interpreting exponential decay functions I exponential ANS: exponential growth; 40%o function exponential growth functions NOT: Example 3 REF: Algebra 1 Sec.6.4 DIF: Level 1 PTS: 1 NAT: HSA-SSE.B.3o I HSF-IF.C.8b I HSF-BF.A'1a I HSF-LE.A.lc KEY: identifying exponential growth and decay functions I interpreting exponential interpreting exponential decay functions I exponential function NOT: Example 3 19, growth functions I I ANS: y = 2800(l'005)2' REF: Algebra 1 Sec. 6'4 Level 1 HSA-SSE.B.3c IHSA-CED.A.2 I HSF-IF.C.7e IHSF-IF.C.Sb IHSF-BF.A.1a IHSF-LE.A.1c IHSF-LE.A.2 application I exponential function I exponential growth function I compound interest NOT: Example 5 PTS: NAT: KEY: I DIF: J ID: A 20. ANS: x=10 PTS: 1 DIF: 1 Level REF: Algebra NAT: HSA-CED.A.1 | HSA-REI'A'l KEY: exponential equation I solving exponential NOT: Exarnple 1 21, 1 Sec' 6'5 equations with the same base ANS: x=2 REF: Algebra 1 Sec' 6'5 DIF: Level 1 PTS: 1 NAT: HSA-CED.A.l I HSA-REI.A'I KEY: exponential equation I solving exponential equations with unlike NOT: bases Example 2 22, ANS: x 7 11 REF: Algebra 1 Sec' 6'5 Level 1 NAT: HSA-CED.A.l I HSA-REI'A'I KEY: exponential equation I solving exponential equations with unlike bases NOT: Example 2 ANS: PTS: 23. I DIF: 23 x=_T REF: Algebra 1 Sec' 6'5 Level I NAT: HSA-CED,A.1 | HSA-REI'A.1 KEY: exponential equation I solving exponential equations with unlike bases NOT: Example 3 ANS: PTS: 24. I q, =2(3)'-'; o, = PTS: 1 DIF: 162 DIF: REF: Algebra 1 Sec' 6'6 1 KEY: application IHSF-LE.A.2 Level NAT: HSF-IF.A,3 IHSF-BF.A.2 NOT: Example 5-1 I geometric sequence 25. ANS: at=9rar=an-r-8 REF: Algebra 1 Sec' 6'7 Level 1 NAT: HSF-IF.A.3 | HSF-BF'A'1a I HSF-BF'A.2 | HSF-LE'A'2 KEY: writing recursive rules for sequences I recursive equation I recursive rule NOT: Example 2 ANS: PTS: 26. 1 DIF: 1 DIF: 4 PTS: Level I REF: Ch 6 Quiz NAT: HSN-RN.A'I IHSN-RN'A'2 NOT: Exercise 5 4 ID: A 27. ANS 1000 PTS: 1 NOT: Exercise 28. DIF: Level 1 REF: Ch 6 Quiz NAT: HSN-RN.A'I |HSN.RN.A.2 DIF: Level 1 REF: Ch 6 Quiz NAT: HSN.RN.A'I |HSN-RN.A.2 7 ANS: 27 PTS: I NOT: Exercise 8 29 ANS: a.y=675(1.005)t2' b. $807.76 DIF: Level2 REF: Ch 6 Test B PTS: 1 NAT: HSA-SSE.B.3c I HSA-CED.A.2 | HSF-BF,A. a I HSF-LE.A.2 I HSF-IF'C'8b 1 NOT: Exercise 30. 11 ANS: a. y=12(2.2)' in', or b. !=2.2t 618.4 in., or 51.536 ft' ft c. 7 times 3I. 1 DIF: Level2 REF: Ch 6 Test B HSF-IF'C'8b HSF-BF.A.1a I HSF-LE.A.2 | HSA-SSE.B.3c I HSA-CED.A.2 | NOT: Exercise 12 ANS: PTS: NAT: a. y = 6599(0.8s)' b. $4793.8s c. $511.84 d. never; An exponential function will approach zero but can never equal zero PTS: NAT: 1 DIF: Level2 REF: Ch 6 Test A HSA-SSE.B.3c I HSA-CED.A.2 I HSF-BF,A. 1a I HSF-LE'A'2 I HSF-IF.C'8b NOT: Exercise 15 5 ID: A 32. ANS: a. exponential growth b 24 18 -18 0 domain: all real numbers; range: y > 0 c. 40% d. about2.SYo e. 120 deer PTS: DIF: Level2 I REF: Ch 6 Quiz NAT: HSA-SSE.B.3o I HSF-IF.B.4 | HSF-IF.C.7e I HSF-IF.C.8b I HSF-LE.A.lc NOT: Exercise 16 33, ANS: neither PTS: 34. I NOT: Exercise ANS: DIF: Level 1 REF: Ch 6 Test B NAT: HSF-IF.A.3 | HSF-LE.A.1a DIF: Level I REF: Ch 6 Test B NAT: 17 geometric PTS: I NOT: Exercise 35, 18 ANS: a. Minuteso x Number of bacteria, y b ! =2' c. 1,048,576 0 t 2 3 4 5 6 1 2 4 8 t6 32 64 PTS: I DIF: Level2 REF: Ch 6 Test A NAT: HSA-SSE.B.3c I HSA-CED.A,2 | HSF-BF.A.1a I HSF-LE.A.2 NOT: Exercise 29 6 HSF-IF.A.3 | HSF-LE.A.1a ID: A 36. ANS: a. exponential growth b. s}%growth c. about3.4Yo d.6750people PTS: I DIF: Level2 REF: Ch 6 Test B NAT: HSA-SSE.B.3c I HSF-LE,A.1c I HSF-IF.B.4 | HSF-IF.C.8b NOT: Exercise26 37. ANS: linear; As x increases by PTS: I 1, y increases by 4. The rate of change is constant. DIF: Level I REF: Algebra 1 Sec' 6'3 NAT: HSF-IF.C.9 I HSF-BF.A.1a I HSF-LE'A.1a I HSF-LE.A.2 KEY: exponential function I identifying exponential functions NOT: Example 38. ANS: exponential; As x increases by 1, 1 y is multiplied by 2. REF: Algebra 1 Sec' 6.3 Level 1 NAT: HSF-IF.C.9 IHSF-BF.A.la I HSF-LE.A.la IHSF-LE.A.2 KEY: exponential function I identi$zing exponential functions NoT: Example I PTS: 1 DIF: NUMERIC RESPONSE 39. ANS: 5lenses REF: Algebra 1 Sec. 6.5 Level I NAT: HSA-CED,A.I I HSA-REI.A.I KEY: exponential equation I solving exponential equations with unlike bases I application NOT: Application-1 PTS: I DIF: OTHER 40. ANS: a. The duration of the eighth note is 2 times longer than the duration of the sixteenth note. b. 30 half notes c. Multiply each note in the table by 32;yes; The number 32 can be expresse d as 25 , so multiply each number in the table by 2t . Because the numbers all have a base of 2,they can be simplified by the Quotient of Powers Property. DIF: Level3 REF: Algebra I Sec' 6.1 PTS: I NAT: HSN-RN.A.2 KEY: application I scientifrc notation I standard fonn of a number I properties of exponents NOT: Application-3 7 ID: A 41, ANS a. v 4 -84 4 8 x -8 b. yes; v x -2.90 asi¡ x -1,62 r. itt. second trade ship; The path of the first trade ship approaches the equator but never travels into any part of the southern Atlantic Ocean. PTS: 1 DIF: Level3 REF: Algebra 1 Sec. 6'5 NAT: HSA-CED.A.I I HSA-REI.A.I I HSA-REI'D.I1 KEY: exponential equation I solving exponential equations by graphing I application NOT: Application-3 I