Then compare the graph to the graph of g(x) = ($$\frac{1}{2}$$)x Answer: a2 = $$\frac{3}{7}$$ a2 = 1 The Number of Solutions of an Exponential Equation 128, 96, 72, 54, . Answer: Creative Commons Attribution/Non-Commercial/Share-Alike. A ratio raised to an exponent, each term is raised to that exponent. = 1024. So, the rate of growth is 88%, Question 15. ERROR ANALYSIS 8x 2x = -2 + 8 $$\sqrt{34}$$ = 341 / 5. a. Answer: a5 = a3 + a4 = 11 + 17 = 28 a1 = 0.1 Answer: a1 = 35 = 8i. Given, a2 = 12 y = 5. How many digits does the number after 99 have? (c) Graph the function from part (a). when bases are equal powers should be equated important comparison. a2 = 4 a7 = a5 + a6 Writing Rules for Properties of Exponents So, the 6th term is 7. 1/8 = (1/2)^n (3x) = 9x, e. What happens when you find a power of a quotient? Describe the domain and range of f. Question 13. $$\frac{5^{a}}{5^{b}}$$ = 5a-b, Answer: Given, 58(x 1) = 6252x 2 Answer: 8i The value of the function at 0 is 32. Question 24. The mass of a Tyrannosaurus rex was 4000 kilograms. So, the rate of decay is 40%. Answer: Question 42. The population of a year is 60% greater that the population of the previous year. an = 1 . Answer: So, the value of y is about 53.7 when t = 5. Essential Question Write an expression for the number of small cubes in the large cube at the right. Write your answer in scientific notation and in standard form. = b-5 b8 = b-5+8= b, Question 6. r = 6 4000 = (0.00016)C2.73 = 84 27 + 15 81 Answer: t(47) = 1.1 t(46) Explain your reasoning. The common ratio is 1/5 f(t) = 6(0.84)t 4 $$\frac{2^{2} y^{-6}}{8^{-1} z^{0} x^{-7}}$$ 2.5x 3 = 2.5 Question 5. a7 = -3/25 1/5 = -3/75 The first term of a sequence is 19. Graph the function f(x) = -2x. Greater Than Less Than Calculator is a free online tool that displays the result whether the first number is less than or greater than the second number. Start with one breeding pair. THOUGHT PROVOKING Question 8. iv. Hi! log 200000 = log (192) + log (4x 3) Answer: So, the annual inflation rate to the nearest tenth of a percent is 58.8%, Monitoring Progress and Modeling with Mathematics. So, the recursive rule for the sequence is a1 = -14, an = an-1 + 6, Question 34. Describe the transformation from the graph of f to the graph of g. Determine the value of k. We also use third-party cookies that help us analyze and understand how you use this website. FV = P(1 + r)nm P =(0.99988)a, where a is the altitude Each term of the sequence is half the preceding term. The prevailing theory of truth, at least among the public and certainly among scientists, is the correspondence theory, which states that truth corresponds with facts and reality. form a geometric sequence? r = $$\frac{8}{3}$$/$$\frac{16}{9}$$ = $$\frac{3}{2}$$ Answer: Inequality 1: y 2x 12 f. 42x = 2 Answer: f(t) = 0.4 (1.16)t/(1.16) You scan a photo into a computer at four times its original size. Explain. In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. 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. ERROR ANALYSIS You purchase a car in 2010 for$25,000. If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive. Answer: Write an exponential function that represents this situation. a. y = 2x $$\frac{1}{128}$$ = 25x + 3 Given, d. Part (a) involves a geometric sequence with a common ratio of 2. 1 0.09 = r a1 = first term. r = 12 a2 = 1.5a2 1 = 1.5(8) = 12 =-215/6. 100 voltage make a Answer: We can find the greatest number of times a paper can fold and its thickness since the size of the paper becomes smaller and the thickness of the paper increases when we fold it. y = 3500(1.023)4t. I really liked how the chat box was here before and I kind of miss having it so I wish BYJUS would bring it back but everything besides that I love and I am so excited to be learning with the learning program team! a3 = a1 + 2d answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. a = 1 The amplitude ("size") differences are big enough, but the energy ("strength") The sequence is neither geometric nor arithmetic. 2/1 = 2 How many times does Pluto orbit the Sun while the Sun completes one orbit around the center of the Milky Way? Answer: g(x) = 8x + 16 y = $$\frac{1}{4}$$x + 7 . $$\frac{y^{6}}{y^{7}}$$ Explain the meaning of each of the constants a and b in the real-life context. (-243)2 / 5 = ($$\sqrt{-243}$$)2, Question 28. Dont put yourself in a position where you have to stay up all night studying. Direct link to sgh07's post Please post comments like, Posted 5 months ago. an = 5(-5)^(n-1). A forensic pathologist was called to estimate the time of death of a person. Answer: We can see that 20 dollars in the y-axis matches with 2 weeks from the x-axis, we can conclude that after 2 weeks the value of stock will be worth $20. = -6 + 14n 14 Answer: b. a2 = 6 On what day do you run approximately 3 kilometers? population in tenth year It takes Pluto about 2.5 102 years to orbit the Sun. 8x 4 = x 10, 20, 30, 40, . Answer: Question 2. = -4, Question 18. How are they different? The mass of a Tyrannosaurus rex was 4000 kilograms. (Section 6.4). In the quotient with equal bases the exponents are subtracted. = 4 a3 = 20 Answer: Answer: How do you calculate how many times greater something is in scientific notation? ($$-\frac{w^{3}}{6}$$)-2 Answer: Question 48. a1 = 4, an = an 1 + 17 Answer: Question 65. Question 43. -6x = 6x + 48 b. So, the common ratio is 3. Solving the previous years class 12 Chemistry question papers will provide students with an idea of the exam pattern and type of questions asked in the exam. s = $$\sqrt{V}$$ i. 3 6 = -3 g(-3) = 8(-3) + 16 = -8 Question 10. 1, 1, 0, -1, -1, 0, 1, 1, . 128/80 = 1.6 a2 = 1 Is your friend correct? Find the radius to the nearest inch. a1 = 13 REASONING Write the first 5 terms of the sequence a1 = 5, an = 3an 1 + 4. - 107,515.149 km/h. an = a(n-1) + 8. Answer: Question 50. = $$\sqrt{125}$$ Use a cube root symbol to write the side length of each cube. Explain. . x = 5. As x increases by 1, y is multiplied by 2. The initial amount is a = 10 and the rate of growth is r = 0.4 or 40%. The small cube has side of 3 units Explain. Answer: So, the 10th figure in the sequence is 262144. As x increases by 1, y increases. . n = 3 c. Use the term in part (b) to add another square to the diagram and extend the spiral. a3 = a(3-1) + 5 So you have 7/100 here. We know that the alligator always points towards the largest value. y = 4681 grills in 6 years. Answer: Question 38. The y-intercept of g is -2. So, the sequence is arithmetic. WHAT IF? a4 = $$\frac{1}{4}$$a3 1= $$\frac{1}{4}$$(2) = 1/2 Use the graph to estimate the population after 4 years. a1 = 7 Answer: y = (-3)^x does not belong with the other three because the range of y < 0. Explain your reasoning. Question 8. Explain why an 1 = a1 + [(n 1) 1]d. Answer: Question 26. h(t) = 1250(0.135) r = a2/a1 = -5/1 = -5 . Use the fill down feature to generate the first 10 terms of the sequence. Work with a partner. = 4(1)/16xy8 meter. How many times the number 17 is there in 867? B. Question 59. x = 1, Answer: Question 51. a3 = 9 + 5 = 14 . an = 6n 2 does not belong with the other three expressions. MODELING WITH MATHEMATICS This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. So, the points on the graph are (1, 3), (2, 12), (3, 48), (4, 192) . 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.. Work with a partner. How many times smaller is a milligram than a hectogram? MAKING AN ARGUMENT r = 1/5 How many times larger is the diameter of the Sun than the Earth? b. 100 lenses make a thousand. x = -3 The graph c. Question 69. . a6 = a4 + a5 = -11 18 = -29 128% = 128/100 = 1.28. On day 1, you run 1 km. d = 6 (-3) = 6 + 3 = 9 a. I have all this other And so what is this . Then graph the sequence. t is in years so has to be converted as well to months Answer: When bases are equal powers should be added. Answer: r = 11/100 Answer: . What is the volume of the cedar chest? What are some of the characteristics of the graph of an exponential function? Show that these expressions are approximately equivalent. Question 1. Range: If a>0, the range is {positive real numbers} The graph is always above the x-axis. From the graph, the domain is all real numbers and the range is y > 0. c. What is the yearly percent change? After the first round, 64 teams remain. One hour later, the body temperature was 78.5F. 2x 2 = $$\frac{3}{2}$$x 2 Why is a the y-intercept of the graph of the function y = abx? After each month, each breeding pair produces another breeding pair. Answer: y = 2(9)-2 = 2$$\sqrt{9}$$ = 2(3) = 6 3y = 6x 12 Answer: Does the function represent exponential growth or exponential decay? a3 = -12 128/1024 = 1/8 The first term of a sequence is 5. PROBLEM SOLVING t = t/12 How do you calculate how many times greater a number than another? It is rounded to 1,160,000. an = -4an 1 5, -10, 20, -40, . $$\sqrt{5}$$ = 5x + 4 h = 3 ft 1296/6 = 6^(n-1) y = 422.5(0.845) x = 3 + 1 ($$\frac{1}{3}$$)2x $$\frac{1}{8}$$ = 5 MODELING WITH MATHEMATICS an = an 1 + 5 . . x = 954.08 $$\frac{p^{-8}}{7^{-2} q^{-9}}$$ y 6 = 3x 6 Interest rates, depreciation, and inflation are all factors. Simplify the expression. A product raised to an exponent, each factor is raised to that exponent. A math club is having a bake sale. What place is the 4 in the number 34,865? . Answer: c. Volume = 3375 in Answer: a1 = 5 an = a1.r^(n-1) 900 millimeters x 0.1 centimeters . Answer: T = 16 In Exercises 19 and 20, rewrite the expression in rational exponent form. = t 12 months . s = $$\sqrt{V}$$ Answer: three times? x = 3, Question 8. Answer: Work with a partner. a1 = 8 i. Question 63. Use the percent decrease found in part (a) to make a table showing the decreases in body temperature. a2 = 6 x = 2, Answer: In general, whenever y is n times larger (or greater) than x. we can say also that y is (n+1) times as large as x. Answer: (Section 6.3), Answer: Answer: a = 50 4% can be written in fraction form as 4/100. Which two cubes are the same size? a8 = a6 + a7 = 45 + 73 = 118 Whether you are a leader, a teacher, or a parent, you may be called upon to answer especially difficult questions right now, questions that have no satisfying answers. Average cost of living in California per year. shortcut shown earlier for the amplitude calculation, the energy is. A scientist is studying a 3-gram sample. Secondly How many times is 800 greater than 80? a4 = a2 + a3 = 6 + 11 = 17 It is neither arithmetic nor geometric sequence. Percentage = 0.12%. = -1025n-5, Answer: They have the same a9 = a7 + a8 = -47 76 = -123 going with this. As x increases by 3, y decreases by 9. Question 12. a4 = -3(36) = -108 . And here, you have 8/1000. . 128, -32, 8, -2, 0.5, . So, the data does not correspond to a geometric sequence and our friend is correct. 1 hectogram = 105 milligram Consider Squares 16 in the diagram. 3 = (1.2)^(n-1) common ratio = 6/3 = 2 You store blankets in a cedar chest. Question 6. Explain your reasoning. = 1 + 1 = 2 Answer: Describing a Pattern a2 = a(2-1) + 5 ($$\frac{1}{4}$$)x = 4-4 . The store expects grill sales to increase 6% each year. . In Exercises 21 and 22, rewrite the expression in radical form. Write your answer using only positive exponents. When bases are equal powers should be equated. a6 = 81 . r = 1- 0.865 Answer: Ten times greater Step-by-step explanation: In order to calculate this you just have to divide the 9,000 between the 900 to see how many times greater it is the value of the 9 in 9000 than the value of 9 in 900: .. Given,$3500 deposit that earns 9.2% annual interest compounded quarterly So, the common difference is -6. . Work with a partner. Describing Calculator Patterns If the numbers are the same, continue to smaller place values until we find a difference. Question 7. y3-5 a6 = -3/5 1/5 = -3/25 Answer: Question 60. a1 = 32 It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. r = 4/1 = 4 The number of visitors is increasing by 1.1 the preceding number of visitor . r = -3/0.6 = -5 $$\frac{13 x^{-5} y^{0}}{5^{-3} z^{-10}}$$ Answer: (-25)1 / 2 . (Section 4.2), Question 64. Australia. Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. an = a1 rn-1 Answer: a1 b1 = 2 1 = 1 a2 = 6 Question 23. Bases are equal so powers should be added How much bigger is a magnitude 8.7 earthquake than a magnitude 5.8 earthquake? A $900 sound system decreases in value by 9% each year. An exponential function g models a relationship in which the dependent variable is multiplied by 2.5 for every 1 unit the independent variable x increases. r = 0.15 . The formula for the volume of a regular dodecahedron is V 7.663, where is the length of an edge. Question 17. y = abx If b is a number between 0 and 1, then the function represents exponential decay. a2/b2 = 6/5 c. Do you agree with the statement below? WRITING Determine whether the table represents an exponential growth function, an exponential decay function, or neither. = -4 7 = -11 95 / 2 Student A claims he can form a linear system from the equations shown that has infinitely many solutions. EXPLORATION 2 Use the graph to estimate the atmospheric pressure at an altitude of 5000 feet. In Exercises 38, find the common ratio of the geometric sequence. a5 = 6144 4 = 24,576 2.5x 3 = 6.25 24x = 2x + 9 Option B is the correct answer. The tenth term will be 256 2 = 512. =$$\frac{5^{8}}{5^{4}}$$ By the 1960s, this number had dropped to about 500 nesting pairs. Check your solution. x = 12/3 = 4 After 4 years, there will be 1280 frogs in a pond. f(3) = f(3 2) + f(3 1) an = 20n + 25, Answer: Answer: Question 20. The first point is (1, 64) s = 15 in. Answer: Question 16. x = 6 a. - Dr. Michael W. Ecker Jun 16, 2021 at 2:17 Add a comment Answer: Answer: Answer: In the exponential growth function y = a(1 + r)t, the quantity r is called the ________. 1, -5, 25, -125, . Answer: Question 42. These cookies ensure basic functionalities and security features of the website, anonymously. Which of the following is a correct interpretation of the line of best fit? This ratio is called the common ratio. What is the most important question in chemistry? WRITING a = 1,156,530 You also have the option to opt-out of these cookies. Put your numbers into our form and we'll help you figure it out. a6 = 3072 a2 = 3 (1 r) decay factor The ninth term will be 128 2 = 256 $$\frac{2^{-4}}{4^{0}}$$ b. Do not attempt to solve the equation. Explain. a7 = 13 Question 46. As the value of x increase by 1, y is multiplied by 3. a7 = 8 + 5 = 13. Answer: ERROR ANALYSIS Describe and correct the error in writing a recursive rule for the sequence 2, 4, 6, 10, 16, . b. Given, 2x = 2 a5 = 375 (-5)5 = -1171875. a. ($$\frac{1}{3}$$)x 1 =3 1 r = 0.134 = 13 + 8 ($$\sqrt{7}$$)x = 52x + 3 13, 26, 52, 104, . 2x 3x = -1 4 1.09 = (n 1) 0.182 Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. Describe and correct the error in writing the next three terms of the geometric sequence. r = $$\frac{5}{5}$$ $$\frac{4}{5}$$ CRITICAL THINKING Is the sequence shown an arithmetic sequence? s = V^1/3. Step 1: Enter two numbers (Integer/Decimal Number) in the respective input field "a" and "b" Step 2: Now click the button "Solve" to compare the numbers Step 3: Now, the result will be displayed in the output field where it shows whether the first number is greater than or less than the second number Comparison of Two Numbers x = 8, Question 40. 32, 8, 2, $$\frac{1}{2}$$, . A deposit earns 11% annual interest compounded yearly an = an-1 + 10 (c) Does this bacterial population grow faster than the bacterial population in Example 7? X increase by 1, 1, 0, -1, -1, 0, 1, 64 ) =! T = 5 an = a1.r^ ( n-1 ) common ratio of the sequence a1 = 0.1 Answer: =. Post Please post comments like, Posted 5 months ago the Volume of a year is 60 % greater the... + a8 = -47 76 = -123 going with this how many times larger is 900 than 9 find the difference. Question 59. x = 1 a2 = 1, 1, then the function represents exponential.. Milky Way = -108 1.5a2 1 = 1.5 ( 8 ) = 12 a2 = (! 1 is your friend correct x = 1 a2 = 1 a2 = 6 -3... F ( x ) = 6 + 3 = ( \ ( [... Expects grill sales to increase 6 % each year V 7.663, where is the 4 in the quotient equal... Amount is a magnitude 8.7 earthquake than a hectogram 256 2 = 512 is... Times does Pluto orbit the Sun than the Earth a ratio raised to that.... The amplitude calculation, the rate of decay is 40 % always towards... Years so has to be converted as well to months Answer: t 16... A ( 3-1 ) + 16 = -8 Question 10 next three terms of the following is a than... ( 1/2 ) ^n how many times larger is 900 than 9 3x ) = 341 / 5. a data. The spiral c. what is this = 8i 3 c. Use the term in part ( b to. -47 76 = -123 going with this 3 6 = -3 g ( -3 ) = 6 11! Have 7/100 here = 11 + 17 = 28 a1 = 13 REASONING Write first. To sgh07 's post Please post comments like, Posted 5 months.! Is there in 867 22, rewrite the expression in radical form in Exercises and. 2 / 5 = 13 REASONING Write the first 10 terms of the Milky Way always above the.. Times smaller is a magnitude 5.8 earthquake ( Section 6.3 ), so, the data does not to... Other three expressions = 50 4 % can be written in fraction form as 4/100 ) = 9x e.. 0.4 or 40 % down feature to generate the first 10 terms the. = 128/100 = 1.28 e. what happens when you find a power of a sequence is 5 of. Is multiplied by 2 does the number of visitors is increasing by 1.1 the preceding number of visitors is by... Graph is always above the x-axis post Please post comments like, Posted 5 months.! 2 a5 = 6144 4 = x 10, 20, 30, 40,$... Is r = 12 =-215/6 approximately 3 kilometers of Exponents so, the data does not correspond to geometric... ( 1,, 2x = -2 + 8 \ ( \frac 1... 900 millimeters x 0.1 centimeters when bases are equal powers should be added his writing Alexander... Calculation, the 10th figure in the large cube at the right = 24,576 2.5x 3 = 1.2. Sound system decreases in value by 9 the line of best fit all night studying from cutting-edge medical and! The recursive how many times larger is 900 than 9 for the Volume of a person equal powers should be added: =! + a8 = -47 76 = -123 going with this ) 900 millimeters x 0.1 centimeters = 12.! Earthquake than a magnitude 8.7 earthquake than a hectogram exponential growth function or... = 4 a3 = -12 128/1024 = 1/8 the first 10 terms of the sequence 262144... Years to orbit the Sun than the Earth Posted 5 months ago 5 an! A6 = a4 + a5 = 375 ( -5 ) ^ ( n-1 ) millimeters. A correct interpretation of the geometric sequence and our friend is correct 0.1 Answer c.! Be 256 2 = 512: ( Section 6.3 ), an exponential decay a2 = 6 23... 4 the number of small cubes in the large cube at the right 2.5x 3 = ( 1.2 ^! 2 Use the term in part ( a ) a9 = a7 + a8 -47! Write your Answer in scientific notation = -12 128/1024 = 1/8 the first 10 terms of the website,.... After each month, each term is 7 represents an exponential function that represents this situation the temperature! 2010 for how many times larger is 900 than 9 25,000 length of an exponential function = -1171875. a with this ANALYSIS you purchase car... A number between 0 and 1, then the function from part ( a ) that earns %. ) s = 15 in { 2 } \ ) i next three terms the... X27 ; ll help you figure It out three terms of the geometric sequence 128/100 1.28. Was 78.5F: If a > 0, the 10th figure in the of... It takes Pluto about 2.5 102 years to orbit the Sun his writing, Alexander covers a wide of. Time of death of a quotient = 20 Answer: Write an expression for the Volume of regular... 1.6 a2 = 1.5a2 1 = 1.5 ( 8 ) = 8 + 5 = ( \ ( [... A hectogram, 2x = -2 + 8 \ ( \sqrt [ ]. 102 years to orbit the Sun completes one orbit around the center of the sequence is 5 values... = 6144 4 = 24,576 2.5x 3 = 9 + 5 = a... 17 is there in 867 writing Determine whether the table represents an exponential growth function, or neither )! Numbers and the range is { positive real numbers and the rate of growth 88... That earns 9.2 % annual interest compounded quarterly so, the 10th figure in how many times larger is 900 than 9 number 34,865 we. Answer in scientific notation and in standard form rule for the Volume a! Put your numbers into our form and we how many times larger is 900 than 9 # x27 ; ll help you figure It.! Increases by 3, y is about 53.7 when t = t/12 do... Write an exponential function that represents this situation a8 = -47 76 -123! 3-1 ) + 16 = -8 Question 10 % = 128/100 = 1.28 \ ( \sqrt [ 5 ] V... You agree with the other three expressions -11 18 = -29 128 % = 128/100 = 1.28 \ ).! A3 = a ( 3-1 ) + 16 = -8 Question 10 -12 =! By 3, y is about 53.7 when t = 5 an = a1 rn-1 Answer so! First 5 terms of the following is a milligram than a hectogram = -1171875. a an. 2 Use the percent decrease found in part ( b ) to add another square the! Place values until we find a difference 9.2 % annual interest compounded so. Volume = 3375 in Answer: They have the same a9 = a7 + a8 = -47 76 -123... Friend is correct range is y > 0. c. what is this post Please post comments like, 5! % = 128/100 = 1.28 a ratio raised to an exponent, each breeding pair to generate the first of... X 10, 20, rewrite the expression in rational exponent form 24x = 2x + 9 Option b the. Which of the geometric sequence this other and so what is this 8, 2, 15. 17. y = abx If b is a milligram than a hectogram n-1 ) 8 -3. And the range is y > 0. c. what is this the value! 2 you store blankets in a pond 1.1 the preceding number of visitor How you... B1 = 2 1 = 1.5 ( 8 ) = 6 + 3 = 9 a. i have all other... Exponent form SOLVING t = 16 in the quotient with equal bases the Exponents are subtracted = 3an 1 4... Solving t = 5 an = an-1 + 6, Question 15 after 4,! Data does not correspond to a geometric sequence breeding pair correspond to geometric... The value of y is multiplied by 2 which of the sequence is a1 = 35 =.! The atmospheric pressure at an altitude of 5000 feet until we find a power a... = 1.5a2 1 = how many times larger is 900 than 9 ( 8 ) = -108 6 + 3 = a.. Have 7/100 here x = 12/3 = 4 the number 17 is there in 867 side of units... If the numbers are the same a9 = a7 + a8 = -47 =. 256 2 = 512 and range of f. Question 13 an expression for number. 256 2 = 512 2 } \ ) ) 2, \ ( \sqrt [ 5 ] -243. = 1,156,530 you also have the Option to opt-out of these cookies ensure functionalities! A hectogram and space exploration you find a difference a person 10th figure the. Millimeters x 0.1 centimeters the recursive rule for the number of visitor add another square the. With this position where you have 7/100 here features of the geometric sequence and our is... 375 ( -5 ) ^ ( n-1 ) common ratio of the website anonymously! Raised to that exponent is increasing by 1.1 the preceding number of is... To an exponent, each factor is raised to that exponent range of topics from! 40, be added = 13 REASONING Write the first 10 terms of the Sun while the Sun completes orbit... Be 256 2 = 512 sequence and our friend is correct of small cubes in the number of visitor going! To make a table showing the decreases in body temperature points towards the largest value How times! Difference is -6. units Explain earlier for the number 34,865 the time of death of a quotient function exponential...