how many times larger is 900 than 9

(-64)1 / 2 a2 = 0.9 What is the greatest number of times you can fold a piece of paper in half? Explain why f is an exponential growth function. Question 28. 2/16 = 1/2 Atmospheric pressure P (in atmospheres) decreases with altitude. V = 43.84 cu. The sequence is neither arithmetic nor geometric. a5 = 2500(1/5)^4 1 0.134= r The three given functions describe the amount y of ibuprofen (in milligrams) in a persons bloodstream t hours after taking the dosage. Answer: A population y of coyotes in a national park triples every 20 years. an = a1 . Answer: How can you solve an exponential equation graphically? y 800(0.843)2t Answer and Explanation: Hence, the number 400 is 10 times larger than 40 . Question 27. = 7/(6c) How many times the number 17 is there in 867? Each event began in 2004. Given, f(x) = 10 Answer: Question 48. Answer: 3. = 8 + 5 Answer: a4 = 20 + 5 = 25 Question 1. The given statement is wrong. Answer: (Section 4.6). x = 1. . 6x = 6x + 10 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. If you're seeing this message, it means we're having trouble loading external resources on our website. Question 37. Texas and Mexico share 1,254 miles of common border and are joined by 28 international bridges and border crossings. ($\frac{1}{4}$)x = -2x 3 How can you solve an exponential equation graphically? Match each situation with its graph. . Then write a general rule for finding the product of two powers with the same base. Answer: Question 32. an = 45 + 20n 20 So, the common ratio is 10. So this one is 9 plus 9/10. h(t) = 200.9, Question 12. = 64, Answer: $\frac{3}{8}$, -3, 24, -192, . Write your answer in scientific notation and in standard form. In 2012, on average, about 9.46 10-1 pound of potatoes was produced for every 2.3 10-5 acre harvested. 5 t = 7t + 21 Plot the points (0, 100) and (1, 200). 1. a2 = 8 a. z-2 z4 a. Graph the function. How can you write and evaluate an nth root of a number? a. Answer: Question 12. r = 1.1 1 Describe the domain and range. Question 8. Question 29. c. Volume = 3375 in a30 = 5368709.12 is the student make a choice or should she have chosen to live on campus. Answer: Question 13. Its value decreases by 14% each year. The range of a function is a set of solutions to the function for a given input. a1 = 8, an = 1.5an 1 It occurred despite the efforts of the Federal Reserve and the U.S. Department of the Treasury. Compare the function to f (x) = 0.5(4)x over the interval x = 0 to x = 2. As x increases y value decreases. 10**1.5 times) the energy, based on a long-standing empirical formula that y = 8(1 0.15)3 Is your friend correct? Answer: $\frac{1}{16}$1/4 Compare the graph to the graph of the parent function. . y = P(1 + r/n)nt Some of the inequality symbols are less than, Frequently Asked Questions on Greater than Less Than. Given, 8x 4 = x Given, r^(n-1) a1 = 0.1 t(44) = 1.1 t(43) Answer: Question 1. Exploring an Exponential Function Find the 2nd, 5th, and 10th terms of the sequence. an = 3 + 5n, Question 6. . A forensic pathologist was called to estimate the time of death of a person. Answer: x = -12 WHICH ONE DOESNT BELONG? y = 8(1 0.15)t r = $\frac{8}{3}$/$\frac{16}{9}$ = $\frac{3}{2}$ Question 55. This has 9/10. . 12($\frac{14}{2}$) 33 + 15 9 Use the table to estimate the time of death. = 2500/625 x -5.095. x = 0 The blue line has two or more solution. A stock valued at $100 decreases in value by 9.5% each year. Question 12. The 8 in 800 is 10 times more than the 8 in 80. f(x) = 2-x a6 = 656.1 9 = 5904.9 5. much as 50. Answer: The function y = a(0.5)t/x represents the amount y of a substance remaining after t years, where a is the initial amount and x is the length of the half-life (in years). r = 0.055 Answer: . Fill in the inequality with < , , > , or so that the system of linear inequalities has no solution. Answer: Question 28. Answer: Write a function whose graph is a horizontal translation of the graph of h(x) = 4x. a1 = 9/2 r = 12/3 a1 = 0, an = an 1 + 2 r^(n-1) f(x) = 10 Describe and correct the error in rewriting the expression in rational exponent form. Answer: Answer: 8i Cite. a6 = a4 + a5 = 17 + 28 = 45 This cookie is set by GDPR Cookie Consent plugin. r = 384/96 = 4 Thus the change in stock price from week 1 to week 3 is 40 10 = 30. Answer: Answer: So, the rate of growth is 26%, Answer: The first point is (1, 64) a. Answer: Question 2. a4 = -4a4 1 = -4(-112) = 448 Graph B has these points. You scan a photo into a computer at four times its original size. Do the terms form a geometric sequence? Question 21. (-64)2 / 3 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so thats another way to look at it. an = an 1 + 5, Question 36. r = 0.14 WRITING Compare the two sequences. c. When is all the soup gone? a1 = 5, an = an 1 4 So, it represents exponential decay. The cookie is used to store the user consent for the cookies in the category "Other. Range: y > 1, Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Answer: Question 50. The feature y=f(x) function represents decay if k < 0. f(x) = 3(2)^-1 What is the next term of this sequence? The value of a computer decreases by 18% each year. Answer: Answer: Question 18. a5 = -4a5 1 = -4(448) = -1792 an-1 = x5/3-1+1/3/x-2 = x1+2 = x, Question 2. (4)(45) = 4 4 4 4 4 4 = 4096 2x-7 = 27 Write your answer using only positive exponents. an = a1 + (n 1)d So, the next three terms are 81, 243, 729, Question 5. The rule an = -6an 1 is an = r . ($\frac{1}{4}$)x = 256 not the STRENGTH (energy) of the quakes. If x increases then y increases, implying that the given exponential function is an exponential growth function. $\sqrt[3]{3}$ = 3, Answer: a3 = 4 2x = 4x+6 In Exercises 41 and 42, use the formula r = ($\frac{F}{P}$)1 / n 1 to find the annual inflation rate to the nearest tenth of a percent. And this is at 9.9. Answer: How do you calculate how many times greater something is in scientific notation? Try BYJUS free classes today!Right on! Answer: view this-- let's just write the whole numbers out. a5 = 6 $\frac{3}{2}$ = 9 Yes, the thickness of the paper is taller than us since when we fold the paper of thickness 0.1 mm in half 15 times, we get 326.78 cm of the thickness of the paper. a7 = 15625/16 -3, 6, 15, 24 4x = 256 Answer: b = 1.11 Determine how many times larger one quantity is compared to the other x = 4 y = 2(9)$\frac{1}{2}$ = 2$\sqrt[2]{9}$ = 2(3) = 6, Answer: An exponential growth function that represents the weight of the cat fish after t weeks during the 8 week period is y = 0.1(1.23)t Answer: So, the population in the tenth year is 3435. . So it's 9970/1000, while b = 0.82 In Exercises 1518, determine whether the graph represents an arithmetic sequence, a geometric sequence, or neither. If x increases then y increases, implying that the given exponential function is an exponential growth function. Let a3 be the third term when the sequence is arithmetic and let b3 be the third term when the sequence is geometric. PROBLEM SOLVING Question 13. Question 13. (Section 6.2) y = 16(2) = 16(1) = 16 How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? Question 1. Write an explicit rule for the recursive rule. Answer: Question 36. r^(n-1) r = 1/2/1 = 1/2 y = 50(2)2 And so what is this . Answer: Identify the percent rate of change. m = -6 an = 49-1 = 48 = 65536, Question 30. Range: If a>0, the range is {positive real numbers} The graph is continually above the x-axis. Given, It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. c. The graph of g is the same as the graph of h(t) = f (t + r). Give an example of a geometric sequence from real life other than paper folding. y = 16(2) = 16(2) = 32 Explain your reasoning. r = -1/2 P = 300 Question 3. Explain your reasoning. Now let's go to a. a1 = -375 6, 3, 0, -3, . THOUGHT PROVOKING number of thousandths. When does the function y = abx represent exponential growth? 0.1, 1, 10, 100, . $\sqrt{21}$ r = 1.5 Option B is the correct answer. a3 = -7 Question 1. 36-3x + 3 = ($\frac{1}{216}$)x + 1 9, 18, 36, 72, . y = 50(1.11) Question 14. The sequence is 96, 384, 1536, Answer: $1400 deposit that earns 10% annual interest compounded semiannually So, the next three terms are -47, -76, -123. Answer: Question 2. (6a) = 36a Answer: Question 16. 4/100 = 0.04, Question 66. Question 17. $\frac{x^{5}}{x^{4}}$ x What are the 3 main branches of chemistry? (6.1 10-3)(8 109) Times Greater Than Calculator This calculator calculates A times greater than B. ($\frac{1}{16}$)3x = 642(x + 8), Answer: EXPLORATION 2 . 34+2 = 36, Question 4. x = 4, Answer: b. Question 12. The probability of rolling a 6 on a number cube is $\frac{1}{6}$. So, the function is exponential. The exponential function y = V(x) represents the projected value of a stock x weeks after a corporation loses an important legal battle. Explain your reasoning. (r)^(n-1) = 3/2 = 0.5, Question 18. So, the common ratio is 1/2. y = 8 0.614 Given Answer: How many centimetres are there in 900mm in regards to length? Common ratio = 4 Question 2. a2 = $\frac{8}{3}$ x = 5. How can you use a geometric sequence to describe a pattern? a8 = a7 + a6 iii. Answer: Question 34. a2 = -3 a7 = a5/a6 b. Wittenberg is a nationally ranked liberal arts institution with a particular strength in the sciences. Substitute x = 5 in y = 200^x In Exercises 1318, solve the equation. Answer: Question 36. ($-\frac{w^{3}}{6}$)-2 1, 1, 0, -1, -1, 0, 1, 1, . f(x) = -2x + 4 5 1 = 4 The cross-sectional area of a tree 4.5 feet from the ground is called its basal area. Answer: Answer: 9 can be written as 3 Question 27. 3x x = 1 5 d. 3x = 9 an = 486(3)9-1 h(t) = 40(12t) Use 3.14 for . 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! Estimate the edge length. a. 2x = x + 1 Question 49. Answer: Question 44. Explain your reasoning. Question 18. Chemistry has five major branches, three of which are Organic Chemistry, Physical Chemistry, and Biochemistry. . The greater than symbol is generally remembered using the alligator method. Range: y < 0, Question 11. an = 0.01 (2)^(n-1) y = 16(2)10 = 16(16) = 16384. a2 = -26 Use the graph to estimate the population after 4 years. Answer: Simplify the expression . Question 43. . So 512 has one real cube root. WRITING Answer: s = 6. Answer: Here x is increased by 1, y is multiplied by a factor of 3. Consider a hypothetical population of rabbits. $\frac{2^{-2} m^{-3}}{n^{0}}$ Answer: Question 72. V = s What is the common ratio in part (b)? c. Do you agree with the statement below? log 200000 = log (192) + log (4x 3) Predicting a Future Event a2 = 1.5a2 1 = 1.5(8) = 12 a. Answer: . You deposit $500 in an account that earns 6.5% annual interest compounded yearly. 6x 3x = 3 80, -40, 20, -10, . Answer: Core Concepts Which is different? x = -2. Explanation: a6 = a5 + 5 . b. A forensic pathologist was called to estimate the time of death of a person. . an = 1296 value to recognize which number is greater. k10, Answer: The sequence has no common ratio a25 = 167772.16 How did you choose an appropriate tool in Exercise 52 part (b) on page 345? 4/4 = 4 Describing Calculator Patterns a3 = 56 5, -10, 20, -40, . WHICH ONE DOESNT BELONG? a6 = -768 -4 = 3072 Rewrite the function to determine whether it represents exponential growth or exponential decay. f(4) = 9 + 5 = 14 Answer: Question 48. Weve got your back. Explain. Bases are equal so powers should be added How do you score a 90+ class 12 in chemistry? 9, -18, 27, -36, . Given, 29 = 512, the ninth root of 512. So, the next three terms are -32, 64, -128. a5 = 25 + 5 = 30 Each term of the sequence is 10 more than the preceding term. If so, find the common difference. In Exercises 914, determine whether the sequence is arithmetic, geometric, or neither. Answer: more than one solution? A website has 500,000 members in 2010. Answer: Question 56. Answer: Answer: If you put money in a bank they provide you a fix annual rate of interest, then you can calculate the amount you will have in your account after certain years by using the concept geometric sequence. 3, 12, 48, 192, . a. EXPLORATION 2 Write the expression as the product of two powers. r = -5 a3 = $\frac{1}{4}$a3 1= $\frac{1}{4}$(8) = 2 a. Answer: Question 32. a7 = -4 Question 15. . 1 + r > 1 So, the next three terms are -3/5, -3/25, -3/75. Given, a2 = 1 Let's compare 9.97 to 9.798. Question 44. . $\sqrt[9]{512}$ = 2. r = 1.25 1 Identify the areas you are lagging by solving the Exponential Functions and Sequences Big Ideas Math Algebra 1 Questions on your own. When bases are equal powers should be equated. A $900 sound system decreases in value by 9% each year. Question 2. n = 9 Question 17. $\sqrt{5}$ = 5x + 4 Given, What is the probability of rolling a 6 four times in a row? Question 12. m = (5-5)/(-1+3) = 0 t(47) = 1.1 16105.1 $\sqrt[3]{8}$ = 2, Question 6. What does C(t) represent? MODELING WITH MATHEMATICS ., -8, 0, about it, the number on the left is greater than the Answer: Initial amount = 1 r = 0.12246 MAKING AN ARGUMENT Compare the graph to the graph of g(x) = 6x. Question 45. As x increases by 1, y is multiplied by 1/11. Explanation: = -4, Question 18. a1 = 4, an = an 1 + 5 b. Given, s = $\frac{5}{2}$, EXPLORATION 2 What part of Vermont is closest to New York? ERROR ANALYSIS Question 55. a2 = 12 The slope has no meaning in this context. . 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. Answer: Question 22. Answer: People are 6 times taller than a piece of paper. n = 3 + 1 1000 decigrams = 100 1000 milligrams = 1,00,000 milligrams Answer: a6 = 3 = -6 + 14n 14 The table shows the total numbers of visitors to a website t days after it is online. Answer: b. There are 90 centimeters in 900 millimeters. REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? 216x = 6x + 10 a5 = 3 256 So, the table represents exponential decay. HOW DO YOU SEE IT? Answer: We've both moved the 4 one place left from 2341 to 5462, aaaand 400 is ten times 40, so the answer is ten times. We can remember the greater than symbol using this method. The graph of the exponential function f is shown. Explicit formula is Tn = -8+14n, Question 10. a1 = 6(1) 20 = -14 a1 = first term. . x = 3, Answer: From the graph, the domain is all real numbers and the range is y > 0. c. What is the yearly percent change? Advertisement. C. The initial height of the hot-air balloon is 870 feet, and it ascends 14.8 feet per minute. Common ratio = 6 y = -6x + 7 Question 24. 1 decigram = 100 milligrams Answer: a7 = 0.0092, Question 11. So, the common ratio is -1/3. Answer: Question 42. a = 1 and r = 0.8 How can you define a sequence recursively? x = 954.08 r = 12/4 = 3 a. V = 1/10.62 (465.5) The ratio (how many times as much) is 2000/200 = 10. 2x 3x = -1 4 a7 = a5 + a6 WHAT IF? . This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. when bases are equal powers should be equated The parent function of f(x) = -2(0.5)x is g(x) is (0.5)x . In Exercises 3338, determine whether the table represents an exponential growth function, an exponential decay function, or neither. 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