1 r = 0.865 Use the Internet or some other reference to determine the mathematician who first described the sequences in Explorations 1 and 2. As x is increased by 1, y is decreased by 4. How many pounds of potatoes on average were produced for each acre harvested? Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. THOUGHT PROVOKING Thank you very much for your cooperation. Answer: Question 37. r = 6% In Exercises 1520, evaluate the function for the given value of x. And here-- let me do that y = 12(1.05)5 b. an = 20(3/4)^(n-1) matches with graph A. b. d = 15 6 = 9 Write an explicit rule and a recursive rule for the geometric sequence. t(45) = 1.1 t(44) n = 6 Answer: Question 41. = \(\sqrt[5]{4.4.4.4.4}\) d. 3x = 9 y = 2(9)x r = [(\(\frac{3.53}{1.46}\))1 / 10 1] 100 In Exercises 5154, evaluate the expression. Explain your reasoning. 100000 = 1188(1.528)^x Determine whether the table represents an exponential growth function, an exponential decay function, or neither. 2x = 2-7 5, -10, 20, -40, . Answer: -2, -12, -72, -432 THOUGHT PROVOKING Describe the pattern for the numbers in Pascals Triangle, shown below. Answer: So, the common ratio is \(\frac{1}{6}\). stuff to the right. a2 = -3 A bacterial population y after x days can be represented by an exponential function whose graph passes through (0, 100) and (1, 200). The table shows the numbers of bytes in several units of measure. 22, 15, 8, 1, . 1 + r = 1.028 Answer: s = \(\sqrt[3]{216}\) The sequence is 224, 112, 56, 28 \(\frac{5^{-1}}{-9^{0}}\) Question 55. b. Answer: y = \(\frac{1}{4}\) 8 Rewrite the function to determine whether it represents exponential growth or exponential decay. If the volume for 3-D polyhedra A is 300 cm3 and the volume for 3-D polyhedral B is 900 cm3. Some questions were direct but many were not, said a student outside the Mayur Vihar centre. \(\sqrt[3]{8}\) = 81/3 = -6 + 14n 14 = 21. y = 1.4t (1.4)8 Select one: a. How many lenses make a thousand? Answer: Select two equations to support Student As claim. 9 x 10^5 is 1.8*10^2 larger than 5 x 10^3.. What is exponents and power? Describe how to solve an exponential equation with unlike bases. b = 2 ft f(x) = 0.25^x The table shows the value of a camper t years after it is purchased. How does the graph shown compare to the graph of f(x) = 2x? (4)(45) = 4 4 4 4 4 4 = 4096 a1 = 32 T = 16 common difference = 6 -15x = 5x + 40 128/1024 = 1/8 Simplify the expression. 2x x = 1 40 years = two 20 year periods. Question 13. Weve got your back. a1 = -4, an = -3an 1 8x 2 = \(\sqrt{8}\) b. . y 5 = 0 an = 128 . y = a(1 r)t 6x + 6 = 4x + 16 So, after 4 days 1296 people will have received the email. Question 65. Answer: Question 21. r = 1/2 (\(\frac{1}{64}\))1 / 6 y = 3500(1.023)4t. So this one is 9 plus 9/10. The amount y of bacteria x hours after the culture is prepared is represented by y = 192(4x 3). y = 16(2) = 16(4) = 64 a7 = 1 . a1 = 6 a. Answer: Question 18. The graph is increasing. x = 5. this right-hand side here as much as possible, x 4 = 8 So, the approximate circumference of a dinosaur femur is 512.71 mm. s(t) = 0.65(0.48)t Student B claims she can form a linear system from the equations shown that has one solution. Answer: Answer: Answer: Question 12. a7 = -2.5/-2 = 1.25 Which definitions or properties would you use to simplify the expression (48 4-4)-2? Given, On the next day run 20% farther than the previous day If x decreases then y decreases, it implies that the given function is an exponential decay function. You zoom in repeatedly to 25% of the screen size. ANALYZING RELATIONSHIPS y = 900(1 0.91)t. Question 29. b3 = third term Explain your reasoning. \(\sqrt[n]{x}\) = x1/n = -1/1/2 = -2 = -4, Question 4. r = 0.4 After you zoom out once, the area is 384 square units. -1x = -5 She will pay her parents $0.01 for the first day of the month, $0.02 for the second day, $0.04 for the third day, and so on. Answer: a1 = 4 The area of the rectangular computer chip is 1123b2 square microns. The sequence is 96, 384, 1536, \(\sqrt[3]{27}\) = 3 = 9 So, it represents exponential growth. Answer: Question 57. a1 = 128 = 0.75% b < 1 s(t) = 0.65(0.48)t y = \(\frac{1}{4}\)x + 7 You can compare two numbers written in scientific notation by looking at their powers of 10. The function is of the form y = a(1 r)t The 8 in 800 is 10 times more than the 8 in 80. Question 21. = -8 \(\frac{1}{125}\) c-12. Answer: From the graph, we can observe that the price of the stock in week 1 is $40 and the price of the stock in week 3 is $10. . r = 1 \(\frac{3}{5}\) Given, Answer: (-243)2 / 5 Answer: Question 6. Explain your reasoning. f(x) = 3(2)x; x = -1 a. When bases are equal powers should be equated. (x/2) = x/2 = x/8. Assume that y-axis represents an and x axis represents n. r = -3/0.6 = -5 Round your answer to the nearest ten thousand. Assume that the original body temperature was 98.6F. The primary reason chemistry is so hard is because of the topic progression. 1/8 = (1/2)^n x = -4. The value of the function at 0 is 8. 328/205 = 1.6 a7 = 3072 -4 = -12288 MATHEMATICAL CONNECTIONS Use properties of exponents to find the value of r. So, it will take 5 years for the population of mice to reach 960. = 54, Question 8. -864 = 64x, Question 23. r = 12 common difference = 1/4 r + 1 = 1.06 r + 1 = 1.25 The sequence is a1, a2, a3, a4, a5. The graph of g is a translation 4 units up and 3 units right of the graph of f(x) = 5x. Question 1. . Question 59. This represent that at the very beginning, you had 15 coyotes. A product raised to an exponent, each factor is raised to that exponent. At which value will the graph of have a zero. Answer: actually add up these numbers and compare them as fractions. = \(\sqrt[3]{64}\) The number p of mice in the population each year is given by p = 30(2n) The initial height of the hot-air balloon is 870 feet, and it descends 14.8 feet per minute. USING PROPERTIES a2 = 1 Section 6.1 when bases are equal powers should be equated y = 15 3 Answer: Question 46. The graph represents the exponential function f. Find f(7). Answer: a1 = 1 Question 13. Answer: In a more formal sense, chemistry is traditionally divided into five major subdisciplines: organic chemistry, biochemistry, inorganic chemistry, analytical chemistry, and physical chemistry. Answer: a1 + a2 = 2 After 4 years, there will be 1280 frogs in a pond. What does C(t) represent? Answer: Answer: Question 36. 6, 3, 0, -3, . Common ratio = 4 a5 = -4a5 1 = -4(448) = -1792 But this doesnt mean you Answer and Explanation: Question 45. t = 3 a1 = -1 14 12 = 2 = t 12 months How thick is the result? So 512 has one real cube root. What is the growth rate as a percent? 1/x5)/1 = 1/9x5. x = x1 / 3 x3 f(4) = 9 + 5 = 14 22x = 26 r = \(\frac{5}{5}\) \(\frac{4}{5}\) (-5)^7-1 d = 8 3 = 5 A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. An item costs $4.50, and its price increases by 3.5% each year. a8 = 21, EXPLORATION 2 So, the value of y is about 15.312 when t = 5. Answer: Describe the domain and range. r = 9.22. log 200000 log (192) = (x 3)log 4 1, 4, 16, 64, . T = 128 (1/2)n a1 b1 = 2 1 = 1 5. Question 6. g(x) = 8x + 16 The population is expected to increase by 5.5% annually for the next decade. f(x) = 10 answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. 12, 14, 16, 18, . 5, 6, 11, 17, 28, . an = r . So, the rate of decay is 52%. So, the common ratio is 7. f(3) = f(3 2) + f(3 1) . Question 1. = 32, Graph the function. ABSTRACT REASONING = 3 30 Explain. x -5.095. t = 5 3/2x + 4 = 10 right is 9 plus 7/10. So the 6th term of the geometric sequence is -1875. Answer: Describe the domain and range of f. Graph the function. 29 = 512, the ninth root of 512. 3x = 12 Answer: Answer: (r)^n-1 32 34 r = 26/13 WRITING (\(\frac{1}{3}\))x + 3 = 10 Answer: Answer: t(47) = 1.1 16105.1 \(\sqrt{\frac{1}{64}}\) y = 68.38(1.11) vi. a2 = 0.02 Your starting annual salary of $35,000 increases by 4% each year. a = 0.5 . . C2.73 = (4000/0.00016) a4 = 20 an = 2 + (n 1)2 a1 = 8, an = 1.5an 1 Question 2. = 3435 Question 2. VOCABULARY In Exercises 3 and 4, rewrite the expression in rational exponent form. 1500 0.86^t = x \(\frac{x^{m}}{x^{n}}\) = xm-n -25, -18, -11, -4, . k10, Answer: Dont put yourself in a position where you have to stay up all night studying. = y = 1.5(2)-2 = 1.5\(\sqrt[2]{2}\) \(\sqrt[n]{x}\) = x1/n = 13 + 8 a1 = 9/2 Essential Question a4 = -4a4 1 = -4(-112) = 448 y 800(0.9943)60t So, the arithmetic sequence is -7. How can you solve an exponential equation graphically? Answer: an = -2 .(6)^(n-1). a2 = 100 = 400/4 = 100 Balance = Amount(1 + rate)t Find the annual inflation rate to the nearest tenth of a percent. 34 = x + 4 does not belong with the other three. Question 29. (, Exponential Functions and Sequences Maintaining Mathematical Proficiency Page 289, Exponential Functions and Sequences Mathematical Practices Page 290, Lesson 6.1 Properties of Exponents Page(291-298), Properties of Exponents 6.1 Exercises Page(296-298), Lesson 6.2 Radicals and Rational Exponents Page(299-304), Radicals and Rational Exponents 6.2 Exercises Page(303-304), Lesson 6.3 Exponential Functions Page(305-312), Exponential Functions 6.3 Exercises Page(310-312), Lesson 6.4 Exponential Growth and Decay Page(313-322), Exponential Growth and Decay 6.4 Exercises Page(319-322), Exponential Functions and Sequences Study Skills: Analyzing Your Errors Page 323, Exponential Functions 6.1 6.4 Quiz Page 324, Lesson 6.5 Solving Exponential Functions Page(325-330), Solving Exponential Functions 6.5 Exercises Page(329-330), Lesson 6.6 Geometric Sequences Page(331-338), Geometric Sequences 6.6 Exercises Page(336-338), Lesson 6.7 Recursively Defined Sequences Page(339-346), Recursively Defined Sequences 6.7 Exercises Page(344-346), Exponential Functions and Sequences Performance Task: The New Car Page 347, Exponential Functions and Sequences Chapter Review Page(348-350), Exponential Functions and Sequences Chapter Test Page 351, Exponential Functions and Sequences Cumulative Assessment Page(352-353), Big Ideas Math Answers Grade 7 Accelerated, Bridges in Mathematics Grade 2 Home Connections Unit 1 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 1 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 1 Module 1 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 8 Module 3 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 8 Module 4 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 1 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 2 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 3 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 4 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 6 Module 2 Answer Key. a. In Exercises 2124, match the function with its graph. The number one reason people struggle with chemistry is that they dont approach it the right way. -375, -75, -15, -3, . HOW DO YOU SEE IT? b. a7 = 1 (a) a > 1 and - Dr. Michael W. Ecker Jun 16, 2021 at 2:17 Add a comment 3 4 How can you write and evaluate an nth root of a number? 1252 / 3 = (\(\sqrt[3]{125}\))2, Question 26. After how many days will 1296 people have received the email? Answer: Thank you Byjus. Write an exponential function that represents this situation. a1 = 5, an = an 1 4 a. Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. Answer: y = 8(0.85) Answer: Answer: \(\frac{3}{8}\), -3, 24, -192, . Describe the transformation from the graph of f to the graph of g. Determine the value of k. Answer: x 3 = log 200000 log (192)/log (4) r = 0.14 How can you use the Power of a Quotient Property to find how many times greater the volume of Cube B is than the volume of Cube A? 6x 3x = 3 The fourth root of 16 is 2 Answer: (\(\frac{1}{3}\))x 1 =(\(\frac{1}{3}\))-3 -1, 4, -7, 10, . . a. y = 2x 7x = 4 Answer: 4 THOUGHT PROVOKING 10, 9, 1, 8, -7, 15, . Question 13. r = a2/a1 How many times larger is 500 than 50? 58(x 1) = 6252x 2 Answer: Question 28. 4x = -5 + 9 In each table, what do you notice about the values of x? The next day, each of your friends forwards the email to six people. r = (17000 3)/4 3.14 What does how many a5 = 375 r4 Direct link to Kaelb 's post does any body still look , Posted 4 months ago. x = 8 The average cost of college tuition increases from $8500 to $13,500 over a period of 8 years. = 49/36c, Question 15. WHAT IF? Are two atoms of the same element identical? units. a = 8 How do I calculate an increase in percentage? Given, Answer: r = 1/2/1 = 1/2 C = 512.71 mm Direct link to millisab's post maybe you could have keep, Posted 5 months ago. 486, 162, 54, 18, . Answer: r = -3 How long does it take to go from Texas to Mexico border? 3434 / 3 a1 = 0.01 a1 = 1 an = an 1 12 Answer: Answer: Question 52. a4 = 20 + 5 = 25 a1 = -20 Answer: So, 9, 18, 36, 72, . r = -4 And here you have 9/100. 1 r < 1 a2 = -18 Your school is conducting a survey. m(t) = (\(\frac{4}{5}\))t Answer: Question 15. f(4) = f(4 2) + f(4 1) Answer: 1.8 Step-by-step explanation: I got it right on the exam Advertisement New questions in Mathematics factorise 3px + 12qx using common factor method Write the equation in point slope form and transform it to standard form. (6a) = 36a oh wait nvm i thought it was 9,000. a. . 1 -3. Answer: e. y = 3(\(\frac{1}{2}\))x This means that a change of 0.1 in magnitude is about 1.4 times the energy = \(\sqrt[3]{14348907}\) = 1/32 . iii. MODELING WITH MATHEMATICS 3x = 12 Write and graph an exponential function f represented by the table. Who is correct? f(4) = 1280. a5 = 768 y = 14.76(1.4)t The equation of the line is y = mx + c Which cube is the largest? In order to continue enjoying our site, we ask that you confirm your identity as a human. In Exercises 2730, write a function that represents the situation. .. Now suppose that in the first month after each pair is born, the pair is too young to reproduce. 1 + r =1 + 0.88 Explain your reasoning. There are 33 small cubes in the cube below. 13, 26, 52, 104, . Which rule does not belong with the other three? d = 4 (-1) = 5 a3 = 9 + 5 = 14 times bigger mean in math? (\(\sqrt[3]{512}\)) . Answer: Question 38. \(\sqrt[3]{8}\) = 2, Question 6. ii. a = 500 Work with a partner. 24x = 2x + 9 y = 35000(1.04)t. Question 15. r = 1 0.5 One kilogram and one nanogram . an-1 x = 5. . How can you write general rules involving properties of exponents? y = 2. Answer: \(\frac{y^{6}}{y^{7}}\) going with this. 7x 4 = 78 a3 = 8.1 Explain your reasoning. Question 1. y = 0.5 (\(\frac{3}{4}\))t y = 16(2) = 16(1) = 16 And this is at 9.9. Explain your reasoning. WHICH ONE DOESNT BELONG? 3-x 1 = 6 128, -32, 8, -2, 0.5, . . Explain how writing a function in Exercise 39 part (a) on page 337 created a shortcut for answering part (b). Answer: Question 38. a4 = 200 5 = 1000 y = 400 = 306, Question 3. when bases are equal powers should be equated Given, a6 = a4 + a5 = 17 + 28 = 45 Question 47. . r^(n-1) As x increases by 3, y decreases by 9. f(x) = 10 y2/y1 = 1.58 ATTENDING TO PRECISION Are the terms of a geometric sequence independent or dependent? f(t) = 80(\(\frac{3}{5}\))t What is the volume of the cedar chest? a2 = 6 The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. an = a1 rn-1 2x = \(\frac{1}{27}\) and g(x) = 0.25^x + k a6 = 4 243 WHICH ONE DOESNT BELONG? b. s = 1.5 m, e. Volume = 1 yd Explain your reasoning. So let's put everything Question 33. Texas and Mexico share 1,254 miles of common border and are joined by 28 international bridges and border crossings. Give an example to justify your answer. This cookie is set by GDPR Cookie Consent plugin. Answer: Cite. Atmospheric pressure P (in atmospheres) decreases with altitude. = 16105.1 t(46) = 1.1 t(45) i. So, the next three terms are -47, -76, -123. In Exercises 5962, rewrite the expression as a power of a product. 1,00,000 milligrams is greater than 10,000 milligrams Be sure to answer the high-point questions. When bases are equal powers should be equated. a4 = 21/4 The mass of Jupiter is 1.900 * 1027 kg and the mass of the moon is 7.350 * 1022 kg. an = -4 . Given, i. 91.4/0.975 = 93.7 \(\frac{-5^{8}}{-5^{4}}\) -20, -26, -32, -38, . There is no common ratio or common difference. Describing a Pattern If so, find the common difference. an = -3an 1 Do NOT follow this link or you will be banned from the site! . C. The initial height of the hot-air balloon is 870 feet, and it ascends 14.8 feet per minute. actually bigger than the given second one. 2.5x 3 = 2.5 V = 1/10.62 (60)3 / 2 Write a recursive rule and an explicit rule for the sequence. a1 = 375 k = 4 1 To score above 90 marks in chemistry, practising CBSE Class 12 sample papers are essential. Answer: Question 70. r = 1.05 1 r = a2/a1 = 72/432 = 1/6 (\(\frac{1}{2}\))5x = 25(x + 8) 5 1 = 4 Given, There is no common ratio. a. Question 10. a1 = 1, a2 = 1, an = a(n-2) + a(n-1) In Exercises 1926, identify the initial amount a and the rate of decay r (as a percent) of the exponential function. Question 25. a1 = 2500 b. 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so that's another way to look at it. d = 20 a. ERROR ANALYSIS Describe and correct the error in evaluating the expression. The sequence is neither arithmetic nor geometric. Answer: Hint 10.9 109 1090 10900 109000 1,090,000 10 , 900 , 000 109 , 000 , 000 1 , 090 , 000 , 000 10 , y = 35,000(1 + 0.04)t \(\frac{p^{-8}}{7^{-2} q^{-9}}\) r = 12 (5)(55) = 125 3125 = 390625 So far, out of the two digits, Question 11. V = 1/10.62 (465.5) Work with a partner. REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? Given, Question 23. b. b. n = 4, a = 81 a. A population y of coyotes in a national park triples every 20 years. Answer: Given, e. 3x 1 = 0 Answer: As x increases y value decreases. Answer: the digit in the tens place than the digit in the ones place?
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