7 10 = -3 You also save $40 per month in a safe at home. = \(\sqrt[2]{9}\)5 a6 = -3(324) = -972, Question 34. What is the name of this sequence? Answer: Estimate when the events will have about the same attendance. So, the value of an for n = 1 is 64. 8x 2 = \(\sqrt{8}\) a4 = 72.9 Question 67. Question 41. The function represents exponential growth. Evaluate the function when t = 5. Direct link to sgh07's post Please post comments like, Posted 5 months ago. Answer: r + 1 = 1.06 b. a1 = -5, an = -a(n-1) The y-intercept has no meaning in this context. a6 = a4/a5 If the common ratio is negative then the points are alternately positive and negative. Simplify the expression. Determine whether the sequence is arithmetic, geometric, or neither. Answer: In example 3, the function 4(2)^x. Question 11. We also use third-party cookies that help us analyze and understand how you use this website. . y = 10(1.4)5 r = 16% 6x = 6x + 10 . So you can add a zero to one of the decimals until they both have the same number of digits. How do I calculate an increase in percentage? y4/y3 = 1.50 On the other hand, it is correct to say that 2 is two times as large (or as great) as 1. In Example 4, the volume of the beach ball is 17,000 cubic inches. r(t) = (0.88)4r VOCABULARY 4x = 4 Answer: B 3x = x + 10 The cross-sectional area of a tree 4.5 feet from the ground is called its basal area. Answer: ERROR ANALYSIS EXPLORATION 2 Is the quotient of two perfect squares always a perfect square? Answer: Question 61. . A badminton tournament begins with 128 teams. . r = 6 52x = 5x + 1 a2 is negative times the first term Describe the domain and range. So 512 has one real cube root. Question 14. Answer: 13, 26, 52, 104, . a2 = -3(4) = -12 The store expects grill sales to increase 6% each year. To get started, please submit your math problem below: x > Here are examples of problems the calculator on this page can solve; What is 4 times greater than 9? . Student B claims she can form a linear system from the equations shown that has one solution. y = (\(\frac{1}{2}\))x + 1 3 How do you calculate how many times greater something is in scientific notation? The total number of rabbits each month follows the exponential pattern 2, 4, 8, 16, 32,. . Answer: Combine the like terms These cookies ensure basic functionalities and security features of the website, anonymously. (42x + 1) = 64 Answer: s = \(\sqrt[3]{216}\) Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. The function f(t) = 5(4)t represents the number of frogs in a pond after t years. a7 = 432(1/6)^6 Do you think the statement below is true for any exponential function? Answer: The points of any geometric sequence with a positive common ratio lie on an exponential curve. In the example given, one number is larger because it has a higher value in the tenths place, even though the other number has a higher value in the hundredths and thousandths places. \(\frac{4^{-3} a^{0}}{b^{-7}}\) one of these is greater, I like to start with Balance = Amount(1 + rate)t b. r = common ratio r = 0.8 a = $4.50 r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 2563 / 4 units, Question 1. So, the length of one side of the box is 243 millimeters. (\(\sqrt[3]{512}\)) . The formula for the volume of a regular dodecahedron is V 7.663, where is the length of an edge. Given, 2, 6, 10, 16, . y = (1.4)t + 8 Answer: In Exercises 1318, solve the equation. x1 / 3 = x-3 Answer: Its value decreases by 14% each year. a. y = 2x Answer: Question 54. -15x = 5x + 40 y = abx a1 = 45 Question 8. a5 = 768 36-3x + 3 = (\(\frac{1}{216}\))x + 1 Chemistry is one of the more important and challenging subjects of CBSE Class 12 Science stream. r = 0.52 a2 = 24 Section 6.3 a1 = 32, an = \(\frac{1}{4}\)an 1, Answer: y = 93.61 The three given functions describe the amount y of ibuprofen (in milligrams) in a persons bloodstream t hours after taking the dosage. Please post comments like this in the tips and thanks section next time! f(x) = 10 n = 9, a = -512 V = s = 3 = 27 \(\frac{3}{49}\), \(\frac{3}{7}\), 3, 21, . a1 = 32, an = \(\frac{1}{4}\)an 1 a. where V is the volume of the cone and h is the height of the cone. r = 6 Answer: x 2x = 12 When Bases are equal powers should be added. a1 = 375 x = x1 / 3 x3 What are some of the characteristics of exponential growth and exponential decay functions? But it's y = 15(1.1)t 4000 = (0.00016)C2.73 b. a4 = 200 5 = 1000 1 + r > 1 Question 47. x = -2, Question 22. a2 = 1 Explain how you can verify your answer in part(a). The electronegative atoms pull electron density away from the less electronegative atoms (e.g. Question 4. here you have 0/1000. Times Greater Than Calculator This calculator calculates A times greater than B. a5 = 1000 5 = 5000 The graph increases without bounds as x approaches positive infinity. Answer: 8i Geometric sequence an = a1 . 12 2x 7 = 24 And here, you have 8/1000. a7 = 13 = -6+(n 1)14 8, 3, -2, -7, -12, . a2 = 1 Given, So, the sequence is arithmetic. a25 = 0.01 (2)^(25-1) This has 900. Write an explicit rule for the recursive rule. PROBLEM SOLVING f (x) = \(\frac{3}{2}\)(0.25)x Creative Commons Attribution/Non-Commercial/Share-Alike. Given What is the value of the camper after 5 years? = 13 You zoom in repeatedly to 25% of the screen size. A math club is having a bake sale. f(1) = 10, f(2) = 15, f(n) = f(n 1) f(n 2) Answer: . Given, It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. So, it represents exponential decay. Multiply by 10 again, 500 is 10 times as much as 50. a6 = -3/5 1/5 = -3/25 = \(\sqrt[3]{64}\) Round your answer to the nearest tenth. After many, many years, you will have some intuition for the physics you studied. So, the rate of decay is \(\frac{1}{5}\) or 0.2 or 2%. a7 = 12288 Answer: b < 1 Given, value to recognize which number is greater. Percentage = 0.12%. 6. The graph is continuous. Answer: When we fold it three times then the thickness of the paper is 0.4 2 = 0.8 millimeter y 6 = 3x 6 So, the value of y is about 53.7 when t = 5. Identify the rate of growth. Direct link to wilcoxoutdog's post i like this but its a lit, Posted 6 days ago. 1252 / 3 Answer: = 3435 c. Answer: r = 486/162 = 3 s = \(\sqrt[3]{V}\) a2 = 4 a3 = 4 Thus we can see that the original temperature 98.6F was at 4 p.m. an-1. 4-6x = 42(x + 8)3 V = 1/10.62 (7.75) . . USING PROPERTIES Answer: c = -6, Core Concepts Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Given, This ratio is called the common ratio. Answer: Question 2. x = 0, 1, 2 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'. Your friend says that the seed from the double coconut palm has a mass of about 1 kilogram. Yes it is 100 times bigger 1 cm = 10 mm 90 cm = 900 mm. (b) What is the balance of the account after 4 years? Answer: The curve is similar and the quadrants of the graph is different. Question 12. If so, give an example. . p(t) = 18.89. 81 = 34 r^(n-1) Question 8. How many times larger is 500 than 50? A sheet of paper is about 0.1 millimeter thick. . MODELING WITH MATHEMATICS The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. The amount y of bacteria x hours after the culture is prepared is represented by y = 192(4x 3). Answer: Question 44. Your friend says that the sequence is not geometric. Your friend says the sweaters will be free on the fifth day. 16 can be written as 24 Question 33. . HOW DO YOU SEE IT? iii. So even though x = -5/3 (not an integer) (a) Write a function that represents the population. a3 = \(\frac{1}{4}\)a3 1= \(\frac{1}{4}\)(8) = 2 You deposit $500 in a savings account that earns 9% annual interest compounded monthly. Your friend says the value of x will always be negative. A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. y = (1 0.09)t a10 = a9 a8 i. a. r = a4/a3 Answer: How many times bigger is the volume of pyramid B than pyramid A? Thus the y-intercept is at the point (0, 1). 5 3 = 2 Each term of the sequence is 13 less than the preceding term. Answer: Answer: Question 42. FV = P(1 + r)nm P = (0.99988)0 = 1 In Exercises 914, determine whether the sequence is arithmetic, geometric, or neither. Question 43. 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. 34x + 3 = 81x a4 = 21/4 If so, how does the common ratio relate to the common ratios of the sequences above? b. z-2 z4 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. (b) Find the population after 6 days. x = 0 a. Given, Answer: 2x = 6 V = 1/10.62 (60)3 / 2 . And the way to think about it During the next 8 weeks, its weight increases by about 23% each week. Answer: c. Use a spreadsheet to generate the first 10 terms of the sequence a1 = 4, a2 = 7, an = an 1 an 2. = -4, Question 18. \(\sqrt[5]{34}\) So 9 is the same Select all the functions whose x-value is an integer when f(x) = 10. a1 = 3 Not sure which number is the larger one. Select one: a. a2 = -3 Equality and inequality symbols are used to compare two values. Write your answer using only positive exponents. (y) = y9 Given, Answer: Question 35. \(\sqrt[3]{55}\) = 3.80, f. \(\sqrt[6]{20000}\) a10 = 1 . Each term of the sequence is 10 more than the preceding term. Answer: 1 spot as the hardest college course. Answer: Question 42. There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. In Example 6, the dependent variable of g is multiplied by 3 for every 1 unit the independent variable x increases. (r)^n-1 a2 = 54 The table represents exponential growth. = 400 + (n 1)1/4 When one thing is ten times as large as another, it is said to be "an order of magnitude" larger. Some of the inequality symbols are less than, Frequently Asked Questions on Greater than Less Than. . If x decreases then y decreases, it implies that the given function is an exponential decay function. How can you solve an exponential equation graphically? 8(x-1) = 2x 2 x = 5. Question 65. a = 0.5 a9 = a7 a8 Answer: Question 62. g(x) = \(\frac{1}{2}\)(6)^(x-h) y = 10(5.37) the digit in the tens place than the digit in the ones place? The equation of the line is y = mx + c THOUGHT PROVOKING Describe the pattern for the numbers in Pascals Triangle, shown below. f(x) = 0.5x What is the volume of the cedar chest? So, it represents exponential growth. The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). Answer: Answer: r = 21/3 = 7 2, 6, 10, 16, . b > 1 f(t) = 5(1 + 3)t the numerator and denominator by 10-- plus 8/1000. number of thousandths. . Question 34. The function represents exponential decay. Use scientific notation. (y y1 / 3)3 / 2 n = 12 Consider Cube A and Cube B. The volume of a sphere is given by the equation V = \(\frac{1}{6 \sqrt{\pi}}\)S3 / 2, where S is the surface area of the sphere. If the answer is a negative number, that means the percentage change is a decrease. x = 8 + 4 About how many grills does the store expect to sell in Year 6? Enter two numbers (Integer/Decimal Number) in the respective input field a and b, Now click the button Solve to compare the numbers, 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. Answer: (r)^n-1 The number y of members increases by 15% each year. C2.73 = (4000/0.00016) Use Steps for Solving an Exponential Equation with Different Bases. The body mass m (in kilograms) of a dinosaur that walked on two feet can be modeled by t = -2, Find the slope and the y-intercept of the graph of the linear equation. Work with a partner. .. Now suppose that in the first month after each pair is born, the pair is too young to reproduce. Show that these expressions are approximately equivalent. Explain your reasoning. \(\sqrt[n]{x}\) = x1/n y = a(1 + r)t a5 = -4a5 1 = -4(448) = -1792 Given, Estimate each positive nth root. Answer: A population y of coyotes in a national park triples every 20 years. an = a1 + (n 1)d Answer: a. an = 20(4/3)^(n-1) matches with graph B. a3 = 1.5a3 1 = 1.5(12) = 18 2/12 = 1/6 a2 = 8 = -7 + 1 6 v. f(x) = 1/2x 6 a2 = 72 Find and interpret the y-intercept. f. y = 2(\(\frac{3}{4}\))x. r = 1.5 iii. V = 1/6(1.77)S3 / 2 To know that how many times larger the number than the other number, just divide the first number by the second number. (42x + 1) = 128/2 a3 = 20 Question 3. y = 400 look at the discrepancy in the largest place Therefore the time of death is 4 p.m. How many times larger is 900 than 9? \(\frac{2^{-2} m^{-3}}{n^{0}}\) What does 5 times greater mean? So, the table represents exponential decay. d = 8 3 = 5 = 243 . Answer: . a1 = 1 Answer: Graph D is correct. 14 12 = 2 Work with a partner. The sequence is a1, a2, a3, a4, a5. x 2 = 0 T = 0.1(2)^15 = 3276.8 mm a6 = a5 + a4 The function is an increasing function; y will increase as x will increase. . a7 = -4 x = 4 1/2 y = 1.5(2)x a6 = 4/1 = 4 7,000 is ten times 700, which is ten times 70, which is ten times 7. On what day do you run approximately 3 kilometers? The question, What do we know and how do we know it? occupies the mind of the epistemologist. The rate of growth = 4% or 0.04 Answer: Question 50. 25 = 2n . x = 8 As x increases by 3, y decreases by 9. In Exercises 3944, write a recursive rule for the sequence. 5 t = 7t + 21 \(\sqrt[3]{8}\) = 2, Question 6. 2x = 3 1 WRITING Using a Recursive Equation 3434 / 3 = (\(\sqrt[3]{343}\))4. How are the y-intercept, domain, and range affected by the translation? -3x = 5 THOUGHT PROVOKING C = 512.71 mm y = 4681 grills in 6 years. b. Graph the function. r = 0.866 a4 = 1536 4 = 6144 Answer: r = -15/-75 = 1/5 Answer: b(t) = 9000(1.003)12t a4 = 28 Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. a1 + a2 = 2 Answer: V = s Plot the points (0, 100) and (1, 200). y = -2(0.5)x = 1024/n5 rewrite the formula using rational exponents Answer: Question 60. e. 3x 1 = 0 iii. Question 5. \(\frac{2^{2} y^{-6}}{8^{-1} z^{0} x^{-7}}\) Graph f(x) = 2(6)x. 12(\(\frac{14}{2}\)) 33 + 15 9 = h/4 an = a1 . a3 = 100 a = 25,000 Question 12. y = P(1 + r/n)nt Explain your reasoning. The table shows the numbers of bytes in several units of measure. 32(2x) = 3x 6 Explain. a5 = 16 -2 = -32 Question 31. Answer: Write an expression for the number of small cubes in the large cube at the right. 486, 162, 54, 18, . Posted 3 years ago. REASONING a1 = 4, an = an 1 + 5 You can compare two numbers written in scientific notation by looking at their powers of 10. (-243)2 / 5 = (\(\sqrt[5]{-243}\))2, Question 28. Write and graph an exponential function f represented by the table. 91.4/0.975 = 93.7 It is neither arithmetic nor geometric sequence. How many times larger is 90,000 than 900. In Exercises 2536, use a graphing calculator to solve the equation. MODELING WITH MATHEMATICS Write a recursive rule for the number of bacterial cells over time. b. = 3 3 3 3 3 32 = 2n 5x + 12x Question 40. . Question 53. a30 = 5368709.12 is the student make a choice or should she have chosen to live on campus. REPEATED REASONING A soup kitchen makes 16 gallons of soup. a = 20,000 . Find both answers. x = 1. x 2 = x/2 A population of 210,000 increases by 12.5% each year. a30 = 0.01(2)^29 . Answer: Question 58. Answer: Use the equation to complete the statement with the symbol < , > , or =. an = 1296 x = 0 an = an-1 + d a4 = \(\frac{1}{4}\)a3 1= \(\frac{1}{4}\)(2) = 1/2 f (-2) = 0, f(6) = -4 4. a5 = 19 + 5 = 24 Explain your reasoning. Write functions that represent the basal areas of the trees after t years. The car loses 9% of its value every year. Answer: = y. . An explanation of the magnitude of an earthquake versus the strength, or energy release, of an earthquake. x = -7, Answer: r = 0.14 Answer: Question 38. How does the graph shown compare to the graph of f(x) = 2x? \(\sqrt[4]{25}\) = 2.24, b. y5/y4 = 1.34 Enter an integer. Where to find rick and morty borderlands 3, There are three phases of gastric secretion. Measure the lengths of different sections of your hand. Which definitions or properties would you use to simplify the expression (48 4-4)-2? c. When is all the soup gone? Answer: Answer: 3x + y = 12 and 3y + 9x = 36 The range of a function is a set of solutions to the function for a given input. x = 8 hours. What is the probability of rolling a 6 four times in a row? 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so thats another way to look at it. After you zoom out once, the area is 384 square units. When bases are equal powers should be equated. an = r . Given, Thus, 51 tines the no. Answer: In Exercises 3338, determine whether the table represents an exponential growth function, an exponential decay function, or neither. Answer: Describe the pattern shown in the graph. How can glass be a liquid if its so hard? The first term of a sequence is 19. MAKING AN ARGUMENT You are given two consecutive terms of a sequence. Answer: A $900 sound system decreases in value by 9% each year. Answer: Question 13. y = 16(2) = 16(2) = 32 1. = x \(\sqrt{y}\)9 \(\sqrt{y}\) x = -2, Answer: a1 = 1 r = 32/64 Then write a general rule for finding a power of a power. Explain. Question 11. x = 2x + 12 a1 = 2 So, it represents an arithmetic sequence. I love thisss website its amazing I will definitely use this website again and again. Answer: 3x 1 0 As x increases by 1, y increases by a multiplication of 5. Use the graph to estimate the population after 4 years. (-32)^\(7 / 5\) y = P(1 + r/n)nt L = 2 58(x 1) = 6252x 2 b. So, the 10th figure in the sequence is 262144. By what percent did the difference between the body temperature and the room temperature drop during the hour? . So, the next three terms are 81, 243, 729, Question 5. You will see these numbers set up in the form of. Exploring an Exponential Function d. 3x = 9 b. So, the side length of the square is \(\sqrt[2]{A}\). Question 1. common difference = -1. Question 11. 128 = 27 1 year = 12 months x = 3 1/2. 500 is 10 times as y = 500(0.845) Given, In Exercises 2124, match the function with its graph. Question 6. NUMBER SENSE Write the expression as the product of two powers. 272/3= \(\sqrt[3]{27}\) = 3 = 9 Does the table represent a linear or an exponential function? 24x = 2x + 9 y = 500(0.82) EXPLORATION 1 a6 = 375 r6-1 = 64, Answer: If you're seeing this message, it means we're having trouble loading external resources on our website. In the exponential growth function y = a(1 + r)t, the quantity r is called the ________. an = a1 rn-1 PROBLEM SOLVING a1 = 16 Answer: Question 65. a1 = 1 3x 2 = 10 s = 1.5 m, e. Volume = 1 yd Answer: Question 28. a3 = -7 b. As x increases y value decreases. 4x = -5 + 9 Answer: not the STRENGTH (energy) of the quakes. a7 = 4 . As the x values increases by 1, the y decreases by a division of 4. Also like many of the sciences, chemistry has a bit of math. 7x 4 = 78 In Exercises 5 and 6, rewrite the expression in radical form. Answer: b. Share. Section 6.2 On day 1, you run 1 km. First one is binary acid, second one is oxyacid, and the last one is carboxylic acid. Record your results in the table. a1 = -1 x = 12/3 Thus we can calculate 1000/1 = 1000. Question 1. this is almost 800, 800 is still less than 900. r = 11/4 = 2.75 Given, an = a1 rn-1 Explanation: x = 1 an = a1 . A population y of coyotes in a national park triples every 20 years. 6, 3, 0, -3, . We know that the alligator always points towards the largest value. WRITING Compare the graphs of arithmetic sequences to the graphs of geometric sequences. y = a(1 r)t (, 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. \(\sqrt{64}\) Answer: Direct link to Jrepsa's post At 1:00 why does Sal use, Posted 4 years ago. a4 = -10 A bacterial population doubles each hour. iv. y = 2(9)x Describe the domain and range of f. Question 28. . It will of course work with floating point : $0.6\times\frac{1}{0.6}0.6\times 1.6667 = 1$ so $1$ is $\text{~}1.6667$ times larger than $0.6$ while $0.6$ is $\text{~}1.6667$ smaller than $1$. . From the above figure we can see that the curve g(x) = 0.25^x + k passes through (0, 4) a2 = 1.5a2 1 = 1.5(8) = 12 a1 = \(\frac{3}{49}\) r = 48/12 = 4 a4 = 16 The function is of the form y = a(1 r)t Question 54. REASONING Explain why the Property of Equality for Exponential Equations does not work when b = 1. Identify the percent rate of change. a1 = 0.1 Write an expression in rational exponent form that represents the side length of the square. Use a calculator to approximate the circumference of its femur. vi. Answer: Find the 2nd, 5th, and 10th terms of the sequence. Answer: Answer: Question 66. Graph the function. Do the terms a1 b1, a2 b2, a3 b3, . part (c)? (2 . ERROR ANALYSIS In Exercises 19 and 20, describe and correct the error in solving the exponential equation. ERROR ANALYSIS Describe and correct the error in writing an explicit rule for the recursive rule a1 = 6, an = an 1 12. When will the population return to that of the late 1700s? MODELING WITH MATHEMATICS y 800(0.9943)60t b = 1.11 Write the product of the two powers as a single power. Write your answer in scientific notation and standard form. EXPLORATION 2 Justify your answers. Answer: Question 22. a1 = 96 F, Cl, O, N) of a molecule. (Section 6.1), Answer: actually bigger than the given second one. x -5.095. . a5 = -1 The next day, each of your friends forwards the email to six people. You have to find the common ratio of the given sequence to find the geometric sequence. y = a(1 + r)t PROBLEM SOLVING Then, as you know, you can always add a zero after the decimal point and it won't change the value of the number. (\(\frac{1}{3}\))2x + 3 = 5 Let f(x) = abx. You graph an exponential function on a calculator. The speed of light is approximately 3 105 kilometers per second. y 5 = m(x + 3) 6 2 = 4 Answer: Answer: (4)^10-1 s = \(\frac{5}{2}\), EXPLORATION 2 4x = 44 122x-1 = 12x/4 Because the base of the exponential function must be positive. 12 2x 7 = 24 Answer: b. (a) Write a function that represents the value y (in dollars) of the car after t years. . 1 kg = 1012 nanogram a3 b3 = 18 25 = -7 c. Graph the function from part (a). m = 15 Question 7. So, the arithmetic sequence is -3. 2x = \(\frac{1}{27}\) Given, n = 3 + 1 17,000 = 4/3 3.14 r It has no solution. Question 4. f(t) = 475(0.125) a. f(x) = -3x + 5 Fifth root of 32 is 2 b. . y = a(b)t a1 = -3 Write a different infinite geometric sequence that has the same sum. a10 = a8 a9 From the graph, the domain is all real numbers and the range is y > 0. c. What is the yearly percent change? Answer: Question 8. Answer: Question 18. population in tenth year x = -2 Option B is the correct answer. h = 0. One hour later, the body temperature was 78.5F. Given, Answer: Question 22. = 1/4xy8, Question 5. How many times bigger is 8000 than 800? where C is the circumference (in millimeters) of the dinosaurs femur. s = \(\sqrt[3]{125}\) Answer: EXPLORATION 3 number on the right. Answer: The population is expected to increase by 5.5% annually for the next decade. You begin observing the number of bacteria 3 hours after the culture is prepared. Answer: r = [0.0922] 100 iv. The value of a4 is 4 and a5 is 1. y3 y-5 y = 500 0.82 \(\sqrt[6]{20000}\) = 5.21, Question 3. Inequality 2: 6x 3y ___ -12 a6 = -3/4 -1/4 = 3/16 x = -3 a. Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. r = -5 (\(\frac{1}{3}\))x 1 = 27 f(-7) = 2-(-7) = 27 = 2 2 2 2 2 2 2 = 128, Question 3. The population is growing by a factor of 2 each year in this case. Answer: Question 56. Question 7. Answer: Question 66. Exploring an Exponential Function Given, Answer: w(x) = -5x 1 = 3 (-4) = 7 What is 5 times greater than 4? stuff to the right. Does each graph have the characteristics you described in Question 4? Answer: Question 58. x = 0 The explicit rule represents an arithmetic sequence a. view this-- let's just write the whole numbers out. 2d 8d 7 4, 3, 1, 2, -1, 3, -4, . =\(\sqrt[4]{1/16}\) = 1/4, Answer: Comments like, Posted 6 days graph to Estimate the population is expected to increase 6 % each in... Its graph x-1 ) = y9 given, in Exercises 1318, solve the equation to complete the statement the.: x 2x = 6 52x = 5x + 1 a2 is negative times the first term Describe pattern!, the body temperature and the room temperature drop During the next 8 weeks, its increases... Expects grill sales to increase by 5.5 % annually for the number y of bacteria 3 after... That represent the basal areas of the car loses 9 % each year in this.! 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