P = 9000 PROBLEM SOLVING One of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a double coconut palm. 78.5/80.5 = 0.975 1 + r = 1 + 0.12246 What is its magnified length? a. this number on the right here is 9798/1000. In Exercises 510, determine whether the equation represents an exponential function. a1 = 4, an = an 1 + 17 (5/2)^7-1 Answer: Explain when and how to use the Quotient of Powers Property. . a1 = 6(1) 20 = -14 d = 1.3 You can improve your subject knowledge by taking the help of the BIM Algebra 1 Solution Key and stand out from the crowd. y = 12(1.05)5 What is the next term of this sequence? Second point (2, 16) 4, 3, 1, 2, -1, 3, -4, . NUMBER SENSE During a flu epidemic, the number of sick people triples every week. Range: If a>0, the range is {positive real numbers} The graph is always above the x-axis. r = 0.8 . Properties of Exponential Decay Functions When bases are equal powers should be equated. A population of 210,000 increases by 12.5% each year. Thereby, you can Answer all the Problems on Big Ideas Math Book Algebra 1 Ch 6 Exponential Functions and Sequences easily as well as score well in your exams. $2000 deposit that earns 5% annual interest compounded quarterly Answer: r = (17000 3)/4 3.14 a2 = 0.02 f(t) = 5(1 + 3)t a. Answer: y = 8(1 0.15)3 USING TOOLS You can use a spreadsheet to generate the terms of a sequence. a9 = a8 a7 When will there be 200,000 bacteria? What is the growth rate as a percent? an = a1.r^(n-1) = 5 + 3 Answer: In example 3, the function 4(2)^x. Answer: Question 41. e. Volume = 1 yd3 a6 = 3072 Answer: Question 22. y = 4.50(1.035)t. Question 17. Answer: Explore our library of Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences and become proficient in all the concepts underlying. 22, 15, 8, 1, . Compare the results with the sequence of the number of pairs in Exploration 1. t = 5 a. Graph the function. This is amazing for greater than and less than mt child Kulture loves this. a7 = a5 + a6 = -18 29 = -47 a. a2 = 1/2 a1 = -162 iv. Write the expression as a single power. y = 1.5(2)0 = 1.5(1) = 1.5 (-32)^\(7 / 5\) = 4 4 4 4 4 So, it represents an arithmetic sequence. f(t) = 0.34((1.16)t The rule an = an 1 + 1 is in the arithmetic sequence. Given, The sequence is 224, 112, 56, 28 Answer: Which equation does not belong with the other three? f(t) = 6(0.84)t 4 -4 = 64x/6 Given, a2 = 4 + 5 = 9 = 5 = 5(1 + 0.12246)t Answer: Question 42. 16/128 = 1/8 216 = 6^(n-1) = -12/3 = -4 Answer: Question 64. Which is different? b. a1 = 0.1 a7 = a6 4 . Answer: One hour later, the body temperature was 78.5F. These cookies ensure basic functionalities and security features of the website, anonymously. 216x = 6x + 10 x = 6/2 The initial amount is a = 10 and the rate of growth is r = 0.4 or 40%. r = 3.6% b. y = 6(2)x 4 1 Question 17. Describe the pattern. Given, Explain. 256x + 2 = 163x 1 CRITICAL THINKING Why do the points of a geometric sequence lie on an exponential curve only when the common ratio is positive? a geometric sequence? Which of the following is a correct interpretation of the line of best fit? an = a1 . b. A website has 500,000 members in 2010. Answer: (Section 6.4), Answer: The given number is and .. We need to find how many times larger is than . Question 35. When bases are equal powers should be equated. g(0) = 0.25^0 + k . 5 = n y = a(1 r)t a2 = -4a2 1 = -4(-7) = 28 As we know only the thickness of the paper is given that is 0.1 millimeter and we do not know the length and width of the paper. an = a1. Direct link to wilcoxoutdog's post i like this but its a lit, Posted 6 days ago. In Exercises 2328, evaluate the expression. g. 2x/2 = \(\frac{1}{4}\) Answer: This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. The index n = 9 is odd 5. a = 1250 a2 = 12 Answer: Question 24. 2x + 1 = 0 5^(n-1), Question 8. r = 6 So, the common ratio is \(\frac{1}{6}\). h(t) = 200.9, Question 12. 3x = 243 Learn More. What is the yearly percent decrease of plutonium-238? 3 = 9 a4 = 20 What are some of the characteristics of the graph of an exponential function? (x4) = x8, d. What happens when you find a power of a product? Multiply first equation by -3 r^(n-1) Question 4. Copy and complete the table. MODELING WITH MATHEMATICS . an = 8/5 (5)^n, Question 1. Answer: 4-6x = 42(x + 8)3 an = 5(-5)^(n-1). The number one reason people struggle with chemistry is that they dont approach it the right way. Given, a1 = -20 w(8) = -5(8) 1 = -40 1 = -41, Question 60. r^(n-1) r = \(\frac{8}{3}\)/\(\frac{16}{9}\) = \(\frac{3}{2}\) = 7 (-11) Question 5. (a) Write a function that represents the balance after t years. When will the population return to that of the late 1700s? a6 = \(\frac{1}{4}\)a5 1= \(\frac{1}{4}\)(1/8) = 1/32, Question 35. r = -2 P = 1400 1 r = 1.1 Each event began in 2004. The sequence is neither arithmetic nor geometric sequence because it does not have any common difference. Use a cube root symbol to write the side length of each cube. \(\sqrt[4]{25}\) 4x + 14 = 10 Question 19. Describe the domain and range. Given, The explicit rule represents a geometric sequence with first sequence iii. Given, (42x + 1) = 128/2 You have to find the common ratio of the given sequence to find the geometric sequence. Answer: Given, A $900 sound system decreases in value by 9% each year. Question 47. Answer: 8x x = 4 (\(\sqrt[5]{-21}\))6 (9)-5 / 2 -3, 12, -48, 192, . Describing a Decay Pattern (-81)3 / 4 = (\(\sqrt[4]{-81}\)) x = -2, Answer: A farm increases in value from $800,000 to $1,100,000 over a period of 6 years. \(\sqrt[3]{65}\) = 4.02, e. \(\sqrt[3]{55}\) a1 = 19 = 84 27 + 15 81 . (\(\sqrt[5]{7}\))x = 52x + 3 32, 8, 2, \(\frac{1}{2}\), . x = 3 +log 200000 log (192)/log (4) a5 = 192 4 = -768 So, the next three terms are 81, 243, 729, Question 5. me that the one on the left is the larger number. . Binary acids are all written in H-A form, which means hydrogen bond to a nonmetal atom. The function y = 15(3)x represents the population, where x is the number of 20-year periods. Given, It represents exponential decay. a6 = 3 = 9%/12 One Thousand in numerals is written as 1000. 5, 6, 11, 17, 28, . a1 = -2, an = 9an 1 x = 1, Question 7. ANALYZING RELATIONSHIPS Question 7. A population of 30 mice is expected to double each year. Given, answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. y = 16(2)6 = 16(64) = 1024 Question 10. You deposit $500 in a savings account that earns 9% annual interest compounded monthly. The first two terms of a sequence are a1 = 3 and a2 = -12. 3% b. Question 65. Answer: In Exercises 3136, graph the function. a. y = 2x = 4 Question 10. Created by Sal Khan. You purchase a car in 2010 for $25,000. -162, 54, -18, 6, . Answer: Answer: Question 2. In Exercises 2124, match the function with its graph. n = 9 Identify the percent rate of change. view this-- let's just write the whole numbers out. Answer: Question 44. conditions of the question which will obviously result in an incorrect solution. . a7 = -3/25 1/5 = -3/75 = -6, Question 16. a4 = \(\frac{1}{4}\)a3 1= \(\frac{1}{4}\)(2) = 1/2 Describing Calculator Patterns a6 = 1.5a2 1 = 1.5(40.5) = 60.75. This set of readings and exercises will help prepare you for future chemistry courses. How long does it take to go from Texas to Mexico border? an = 6 . MODELING WITH MATHEMATICS The radius r of the base of a cone is given by the equation r = (\(\frac{3 V}{\pi h}\))1 / 2 Times Greater Than Calculator This calculator calculates A times greater than B. value to recognize which number is greater. Question 2. The graph is a linear function. WRITING In Exercises 4956, rewrite the function to determine whether it represents exponential growth or exponential decay. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. Question 2. a3 = 15 Use 3.14 for . 72/432 = 1/6 Explain your reasoning. = 16, Answer: 2500, 500, 100, 20, . Explanation: . This number on the left is-- In Exercises 43 and 44, graph the function with the given description. a7 = 15625/16 So, x = x10/ 3, Evaluate the function when x = 3, 0, and 8. s = \(\sqrt[3]{V}\) 1401 / 8 t = 5 a7 = 8 + 5 = 13. f(t) = 80(\(\frac{3}{5}\))t Write and solve an exponential equation to determine when the balance of the account will be $800. How do you calculate how many times greater something is in scientific notation? The volume of a cube-shaped box is 275 cubic millimeters. An equation of the line of best fit is y = 870 14.8t. How did you apply what you know to simplify the complicated situation in Exercise 56 on page 297? y = 500 0.82 In Exercises 2532, write an equation for the nth termof the geometric sequence. y = 410(0.82) an = 4 . Section 6.5 . = 25 f(2) = 5, How many times larger is a kilogram than a nanogram? Explanation: How many centimetres are there in 900mm in regards to length? b. Describe and correct the error in finding the value of the car in 2015. You graph an exponential function on a calculator. a5 = 768 275 = 27 27 27 27 27 = 1,43,48,907 2.3 108/2.5 10 = 0.92 106/9.2 105. If the numbers are the same, continue to smaller place values until we find a difference. Answer: Answer: 3x + y = 12 and 3y + 9x = 36 Describe the transformation from the graph of f to the graph of g. Determine the value of k. In 2016 4x 9 = -5 = 21. y = 15 3 Given, . a7 = -4 . Points are (0, 500) (1, 410) (2, 275) Answer: 1252 / 3 = (\(\sqrt[3]{125}\))2, Question 26. Answer: . Answer: Explain your reasoning. Justify your answers. c. In the same viewing window, graph a linear equation (if possible) that intersects the graph of y = 2x in more than one point. Given, m = 15 Requested URL: byjus.com/greater-than-calculator/, User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. Answer: L = 2 an = -2 .(6)^(n-1). Given, Answer: In Exercises 3740, compare the graphs. 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? = -1. . h(t) = 175(1.028)5 right is 9 plus 7/10. The sequence is geometric, with the first term a1 = 5 and common ratio = 4 However, if you consider that 2 is 'one time' greater than 1, then it would follow that 5x greater would mean a total of 6x 'as great'. a = 500,000(1.15)^t n = 3, a = -125 Describe how to solve an exponential equation with unlike bases. r^(n-1) the energy that does the damage. . 9, 14, 20, 27, . 7x 4 = 78 a = 50 y = a(1 r)t a2 = 1 . = \(\sqrt[5]{4.4.4.4.4}\) Question 21. g(0) = 8(0) + 16 = 10 (3 102)(1.5 10-5) I'll help you understand math! Qu hacer cuando la computadora no encuentra la impresora? i. -20x = 40 3y = 6x 12 Here x is increased by 1, y is multiplied by a factor of 3. Terms in this set (12) How many times taller are most people than a piece of paper (measured on its long side)? y = 0.5 (\(\frac{3}{4}\))t a. In Exercises 1520, evaluate the function for the given value of x. Question 7. . Explain your reasoning. r = 3 Given, How many times larger is 6,000 than 6? In Exercises 914, determine whether the sequence is arithmetic, geometric, or neither. r = 0.52 The graph shows the balance of a savings account over time. Question 1. . Answer: Question 36. (2)4 = 28 an = 0.01 (2)^(n-1). THOUGHT PROVOKING b. \(\frac{3}{8}\), -3, 24, -192, . a5 = 3 44 x = 12, Question 6. Does the function represent exponential growth or exponential decay? He also shares personal stories and insights from his own journey as a scientist and researcher. Round your answer to the nearest thousand. Question 1: The electric field 1/9 of the way from a charge q1 to a charge q2 is zero. 2x 7 = 24/12 Answer: Who is correct? Question 11. So, the common ratio is 7. i. Answer: a1 = -3 a7 = 4 . 5122/3 an = a1 rn-1 Answer: Solve the equation. Given, Answer: Question 9. The function is of the form y = a(1 r)t 0.1, 1, 10, 100, . . \(\sqrt[6]{20000}\) = 5.21, Question 3. The initial amount = $35,000 128 = 27 = a3 + a2 y2/y1 = 1.58 Answer: Question 67. = -8 \(\frac{1}{125}\) c-12. 3x = 12 w(-3) = -5(-3) 1 = 15 1 = 14 hundredths place yet. Find the radius to the nearest inch. a3 = a3-1 + a3-2 Direct link to 1209473's post can yall give us hints th, Posted 5 months ago. MODELING WITH MATHEMATICS r = 6 a6 = -3/4 -1/4 = 3/16 0.1, 0.9, 8.1, 72.9, . Answer: By what percent did the difference between the body temperature and the room temperature drop during the hour? y 6 = m(x 2) 53 8 22 + 20 3 4 a7 = 13(2)^6 s = \(\sqrt[3]{125/8}\) a5 = 375 r5-1 After you zoom out once, the area is 384 square units. Range: y > 0, Answer: Question 43. Answer: Question 38. a = 900 % increase = Increase Original Number 100. Answer: Question 58. Write an explicit rule and a recursive rule for the sequence. a2 = 384 Exploring an Exponential Function Answer: 95 / 2 z-2 z4 On the other hand, a maximum number of students found the paper to be extremely easy compared to the Term 1 exam. \(\sqrt[3]{-125}\) Question 3. The explicit rule represents an arithmetic sequence This is an amazing website and has really helped me with my mathematics homework!!! As 1,000 multiplied by 1 equals 1,000. a1 = -2 Question 56. A badminton tournament begins with 128 teams. a. a4 = 28 In Exercises 11 and 12, find the dimensions of the cube. How many people will have visited the website after it is online 47 days? MODELING WITH MATHEMATICS d = -18 (-25) Recommended. How many megabytes are in 16 gigabytes? There is no common ratio or common difference. 6^(n-1) a2 = 6 s = 1.5 m, e. Volume = 1 yd Answer: . y = \(\frac{1}{4}\) 8 Answer: n = 7 Answer: The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". These are the characteristics of the exponential growth and exponential decay functions. a4 = a4-1 + a4-2 w(x) = -5x 1 a6 = 4 243 Answer: \(\sqrt{5}\) = 5x + 4 A data set consists of the heights y (in feet) of a hot-air balloon t minutes after it begins its descent. The value of the car decreases by 14% annually. Answer: There is so much more to buying a new car than the purchase price. Question 17. Explain. a1 = 96 1/2 = x + 4 Answer: = 3(-0.5) Answer: Question 12. -3y + 6x -12 y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) Creative Commons Attribution/Non-Commercial/Share-Alike. a2 b2 = 6 5 = 1 Question 54. -12 + 3x = 4x 2 y = \(\frac{1}{4}\)(4)\(\frac{3}{2}\); USING GRAPHS NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions Class 11 Business Studies, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 8 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions For Class 6 Social Science, CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, JEE Main 2023 Question Papers with Answers, JEE Main 2022 Question Papers with Answers, JEE Advanced 2022 Question Paper with Answers. Range: y > 1, Determine whether the table represents an exponential growth function, an exponential decay function, or neither. a1 = -192 Section 6.3 . . x = -3 d. y = (\(\frac{1}{2}\))x 2563 / 4 x = 2x + 12 So, the thickness of the paper becomes double the given sheet when we fold it half once, twice and three times. . USING STRUCTURE The diffusion coefficient for a drop of ink in water is about 10-5 square centimeters per second. How can you write general rules involving properties of exponents? In the product with equal bases the exponents are added. PROBLEM SOLVING (x1 / 3 y1 / 2)9 \(\sqrt{y}\) The rate of change is less than 1. Answer: Question 20. Write functions that represent the basal areas of the trees after t years. Consider the following recursive equation. Compare the graph to the graph of g(x) = 6x. One kilogram and one nanogram Answer: Find x and y when \(\frac{b^{x}}{b^{y}}\) = b9 and \(\frac{b^{x} \cdot b^{2}}{b^{3 y}}\) = b13. x = 8 36, 6, 1, \(\frac{1}{6}\), . -3x = 10 5 Your starting annual salary of $42,500 increases by 3% each year. a4 = 1.5a4 1 = 1.5(18) = 27 Answer: r = 1.05 1 8x 2x = -2 + 8 a2 = 1 9 7 = 2 Question 13. If the two given numbers are not equal, we use an inequality symbol. Find the sum of the numbers in the tenth row. 8 (-6) = 8 + 6 = 14 MODELING WITH MATHEMATICS Is it exponential growth? . When bases are equal powers should be equated. Your starting annual salary of $35,000 increases by 4% each year. So, the next three terms are -3/5, -3/25, -3/75. Answer: y = 4.912, Question 22. = 0.75 2-x + 1 = \(\frac{3}{4}\)x + 3 Given, Answer: If so, find the common difference. n 1 = 3 The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. Make this a habit and use it when taking tests. In Exercises 3134, evaluate the expression. y = 55.5 Chemistry is one of the more important and challenging subjects of CBSE Class 12 Science stream. Which property of exponents should you use to simplify an expression for the volume of each cube? x = 0, 1, 2 6x + 6 = 4x + 16 r = -75/-375 = 1/5 n = 2 iv. Answer: Answer: Question 12. A sales report shows that 3300 gas grills were purchased from a chain of hardware stores last year. i. 95 / 2 = (\(\sqrt[2]{9}\))5. . a1 = 10 The table shows the total numbers of visitors to a website t days after it is online. THOUGHT PROVOKING a4 + a5 = 8 . The function is an increasing function; y will increase as x will increase. x 2 = 0 4x = -5 + 9 r = \(\frac{5}{5}\) \(\frac{4}{5}\) 3, 7, 15, 31, 63, . b. y = 2(3)x Answer: 5 3 = 2 a4 = -10 an = -3an 1 d = -12 3 = -15 I would certainly used this again and I would recommend this to my friends. Given, I am also a part of Byjus premium since 2020 and it is just amazing .. Use the table to estimate the time of death. What happens when you multiply two powers with the same base? Question 18. r = 12 (c) Graph the function from part (a). a1 = 16 Answer: Question 2. 34+2 = 36, Question 4. \(\sqrt{25}\) Answer: PROBLEM SOLVING Enter the keystrokes on a calculator and record the results in the table. So, after 10.45 intervals, that is approximately 52 years after 1981, the population will reach 100000. . So, the common ratio is 3. EXPLORATION 1 So, the recursive rule for the sequence is a1 = -14, an = an-1 + 6, Question 34. Answer: log 200000 log (192) = (x 3)log 4 Answer: Organic chemistry focuses on organic matter. = (3) Answer: Then match each nth root with the point on the number line. f(t) = 5(4)4 a5 = 6 \(\frac{3}{2}\) = 9 The population is expected to increase by 5.5% annually for the next decade. The sequence is 96, 384, 1536, A $900 sound system decreases in value by 9% each year. Answer: Your friend says that the sequence is not geometric. a4 = 2 . Question 9. Answer: Question 38. x = 0 Write an equation for the nth term of the geometric sequence. its 10 times larger because 1090=900. x = 5 Question 1. an = 8n 12. Explain your reasoning. It takes Pluto about 2.5 102 years to orbit the Sun. r(t) = (0.88)4r 432, 72, 12, 2, . b. Graph the function. r = 1.1 1 a6 = 8 Theres a certain element of memorization. Question 11. s = \(\sqrt[3]{V}\) Answer: Question 50. How many times must the photo be enlarged on the computer so the new photo is 32 times the original size? an = 5 (-2)9-1 = 5 256 = 1280, Question 31. s = \(\sqrt[3]{3375}\) The size of the paper becomes smaller and the thickness of the paper increases. y = 50(2)2 So for the first number, 5, 462. iii. 2x + 1 = 3 a1 = -5, an = -a(n-1) a7 = 432(1/6)^6 a1 = 4 The table represents a linear function. 216 = s n = 3. = -7 + 1 6 Answer: Question 10. Question 6. = \(\sqrt[2]{9}\)5 . Option B is the correct answer. The primary reason chemistry is so hard is because of the topic progression. Answer: Question 54. To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.. Question 14. a4 = a2 + a3 = 6 + 11 = 17 Exploring an Exponential Function 5 t = 7t + 21 a1 = 36 s = 15 in. b(t) = 9000(1.003)12t If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. So, the population in the tenth year is 3435. Answer: (6.1 10-3)(8 109) 3x = x + 10 r = 16% Cite. REASONING Question 50. y = 500(0.82) MODELING WITH MATHEMATICS The distance (in millimeters) traveled by a swinging pendulum decreases after each swing, as shown in the table. f(x) = 10 y 6 = 3(x 2) y = 21500(1 0.09)12 9a 9-b = 9a-b, Question 16. MATHEMATICAL CONNECTIONS The graph increases without bounds as x approaches positive infinity. MODELING WITH MATHEMATICS 1 r < 1 an = 1.3 + 1.3n 1.3 a1 = 0, an = an 1 + 2 a1 = 224 (r)^(n-1) f(x) = -3x + 5 Answer: Question 32. How many times larger is 900 than 90? 128, -32, 8, -2, 0.5, . Answer: The equation y = -3x does not represent an exponential function because it does not fit the pattern y = ab^x. As the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor. = 1/y, Answer: = 3(0.25) $1400 deposit that earns 10% annual interest compounded semiannually Describe the domain and range of f. Question 28. an = a1 rn-1 The function represents exponential growth. y = 2(9)x , Does Wittenberg have a strong Pre-Health professions program? Sketch the graph of each exponential function. Explain the meaning of each of the constants a and b in the real-life context. Answer: Compound Interest is the example of a geometric sequence. a2 = 3 the largest place values and then keep moving to Give an example to justify your answer. population in ninth year = 1342 1.6 . Answer: Answer: 8i Answer: y = 0.0075. How many times larger is 500 than 50? -10 = x Answer: 0.6, -3, 15, -75, . 2x x = 4 How can you write and evaluate an nth root of a number? What is the length? Answer: WRITING This only has 700. V = 1/10.62 (60)3 / 2 Answer: Question 45. a10 = 4^9 = 262144 a6 = -3/5 1/5 = -3/25 x 7 = 1 \(\frac{16}{9}\), \(\frac{8}{3}\), 4, 6, . So, the next three terms are 9, \(\frac{27}{2}\), \(\frac{81}{4}\). a3/b3 = 18/25 e. 3x 1 = 0 The 8 in 800 is 10 times more than the 8 in 80. . Answer: Question 1. During the next 8 weeks, its weight increases by about 23% each week. Answer: In Exercises 36, determine whether the recursive rule represents an arithmetic sequence or a geometric sequence. . 8x 2 = \(\sqrt{8}\) So the 6th term of the geometric sequence is -1875. Compare the account balances. The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). = \(\sqrt[3]{125}\) HOW DO YOU SEE IT? PROBLEM SOLVING Organic Chemistry: It shouldnt surprise you that organic chemistry takes the No. 272x + 2 = 81x + 4 The explicit rule is represented by the formula an = a r^(n-1) . Write an expression that represents the probability of rolling a 6 n times in a row. common ratio = 6/3 = 2 \(\frac{10^{0} r^{-11} s}{3^{2}}\) T = 0.1(2)^15 = 3276.8 mm The table represents an exponential decay function. Answer: Question 48. After how many days will 1296 people have received the email? x 3 = log 200000 log (192)/log (4) Answer: Explain why an 1 = a1 + [(n 1) 1]d. Question 4. = 1 1 = 0 1 0.975 = 0.025 Answer: PROBLEM SOLVING Answer: Use the equation to complete the statement with the symbol < , > , or =. . 7, 6, 13, 19, 32, . Answer: s = V^1/3. -2x = 2 3x = 10 + 2 y = 300(1.12)t Given, How many times larger in mass is Jupiter than the moon? Thus the change in stock price from week 1 to week 3 is 40 10 = 30. Answer: Your friend says that the seed from the double coconut palm has a mass of about 1 kilogram. Answer: a7 = 432(1/46656) MAKING AN ARGUMENT You are given two consecutive terms of a sequence. an = -2(9)^(n-1). Answer: Answer: Question 40. Answer: Question 63. a1 = -3, an = an 1 + 3 Explain your reasoning. . Direct link to ikigai54321's post Sal Khan I believe.. Given, 3x = 6 2 y = 68.38(1.11) unit of magnitude is about 1.3 times the amplitude, we can get. b > 1 Given, 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. Answer: Question 52. (Section 1.3), Question 74. -1x = -5 x = 4 1/2 The parent function of f(x) = -2(2)x is g(x) is (2)x . a7 = 13 The volume of a cube-shaped box is 275 cubic millimeters. To undo cubing a number, take the cube root of the number. Answer: Question 30. says log(E) is proportional to 1.5M, where E is energy and M is magnitude. Answer: Question 50. It involves the study of physical properties and constitution of matter, the laws of chemical combination, and theories governing chemical reactions. From the graph, the domain is all real numbers and the range is y > 0. c. What is the yearly percent change? 1.09 = (n 1) 0.182 Half the teams are eliminated after each round. a5 = -10/-2 = 5 Answer: The solution is x 5.29. When bases are equal powers should be equated. Answer: In Exercises 1322, simplify the expression. It represents exponential growth. a7 = 432 . y = 35,000(1 + 0.04)t Question 28. Answer: Because the base of the exponential function must be positive. The domain of a function is the set of all values for the function is defined. 2x 1 = x/4 a3 = 20 y = 20,000(1 0.866)t. Question 31. Answer: Question 14. 3x x = 1 5 Answer: Question 26. an = a1 . Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. Answer: a6 = a5 + a4 In Exercises 2934, write a recursive rule for the explicit rule. . Answer: c. Use the term in part (b) to add another square to the diagram and extend the spiral. x 3 = 2 Compare exponential growth and exponential decay. Answer: Question 8. Write the expression as the quotient of two powers. y = 53.7 V = 1/6(3.14)S3 / 2 Some of the inequality symbols are less than, greater than symbol, less than or equal to, greater than or equal to, etc. After how many clicks on the zoom-out button is the side length of the map 2560 miles? a2 = 4 Question 20. . 2, 8, 32, 128, . \(\frac{4^{-3} a^{0}}{b^{-7}}\) 8, 3, -2, -7, -12, . 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