IM2 Unit Study Guide

Transcription

1 Name: ate:. Write the next three numbers in the sequence. 2, 0, 50, 250,,,. 5. Sheila started the geometric pattern shown below., 3, 9, 27,? If the pattern continues as shown, what is the next term in the pattern? A Study the number sequence below. 6, 9, 24, 3,... What is the seventh term in the sequence? A What is the first term in the exponential sequence below?!,,, 8, 243, 729,... " 3. Look at the sequence. A , 3, 0.6, 0.2,... What is the next number in the sequence? A Look at the recursive formula. A =6 4. Sam began a pattern with 4 and 7. He added them to get, the third term. To get each term after the third, he added the two preceding terms. 4, 7,, 8, 29,... What is the 9th number in this sequence? For n>,a n = A (n ) +4 What are the first 4 terms of this sequence? A. 5, 6, 7, 8. 6, 0, 4, 8. 9, 2, 5, 8. 0, 4, 8, 22 A page

2 8. The sequence below shows the first five pentagonal numbers., 5, 2, 22, 35,... Each number in the sequence is generated using n(3n ) the expression, where n is the position 2 of the number in the sequence. What is the tenth number in the sequence? A This list shows the first four terms of a geometric sequence. 4, 2,, 2,... Which function can be used to determine the nth term of this sequence? A. f (n) =4 2 n. f (n) =4 2 n. f (n) = 4( 2 )n. f (n) = 4( 2 )n 2. Sandra wrote the sequence below. 9. Generate the 5 th th terms of a sequence if A = 2 and A (n+) =(A n ) 2. 2, 5, 0, 7,... Which equation represents the rule for finding the n th term of this sequence? A. a n = n +. a n =2n 2. a n = n 2 +. a n =2n + 0. The first four terms in a sequence, and the rules that define them, are shown below. a =4 a 2 =2a +3 a 3 =2a 2 +3 a 4 =2a 3 +3 What is the value of a 4, the fourth term shown in the sequence above? A Which expression is the nth term of the quadratic sequence shown in the table below? Term No Value A. n 2. 2n 2. n n 2 +2 page 2

3 4. What is the nth term in the arithmetic series below? A. 4n n 8. Which expression represents the nth term in the sequence, 3, 5, 7, 9, n...? A. n 2. 2n 2. 2n. 2 n. 2n +. 4n 5. Which function describes the sequence 3, 6, 2, 24,... for n =, 2, 3,...? A. f (n) =3n. f (n) =n f (n) = 3(2 n ). f (n) =(n ) The sequence below shows the total number of days Francisco had used his gym membership at the end of weeks, 2, 3, and 4. 4, 9, 4, 9,... Assuming the pattern continued, which function could be used to find the total number of days Francisco had used his gym membership at the end of week n? 6. Which rule applies to the table below? x y A. f (n) =n + 5. f (n) =5n. f (n) =5n + 4. f (n) =n 2 A. y =9 3 x. y =3 9 x. y =3 # 9 $ x. y =9 # 3 $ x 20. What is the sum of the infinite geometric series 7. Which function forms a geometric sequence when x =, 2, 3,...? ? A A. f (x) =x + 2. f (x) =x 2. f (x) =x f (x) =2 x page 3

4 2. Use this diagram to answer the following question: 22. The diagram shown below represents the path of a ball that is dropped from a height of 8 feet. On its first bounce, the ball rebounds to a height of 2 feet; on its second bounce, it rebounds to a height of 8 feet. The tower is 5 cubes high. a) How many cubes are needed to build this tower? b) How many cubes are needed to build a tower like this that is 2 cubes high? c) reate a function to calculate the number of cubes needed for a tower n cubes high. a) Show that the ratio of the height of ounce to the starting height is equalto the ratio of the height of ounce 2 to the height of ounce. Show your work or explain how you obtained your answer. b) ounce, b Height, h (in feet) 0 (Starting height) If the pattern in the table continues, complete your table to show the height of bounces 3, 4, and 5. c) ased on the pattern shown in the table, if h is the height of a certain bounce, write an expression that represents the height of the next bounce in terms of h. d) ased on the pattern shown in the table, write an equation that represents the relationship between height, h, and bounce, b. page 4

5 23. If log 0 x = 2, what is the value of x? q q A. x = 0. x = 0. x = 00. x = ar epreciation enicia purchased a used car for $6400. She estimates that each year she owns the car it will depreciate (lose value) by 2% of its value in the previous year. Part of the table she made is shown in your answer booklet. a) According to enicia s estimate, what amount will be the value of the car 2, 3, and 4 years from the date of purchase? omplete the table in your answer booklet. b) If her car continues to depreciate according to enicia s estimate, by what percent will the value of the car have decreased 3 years from the date of purchase? Show your work or explain how you found your answer. 24. If log x y = 2, which of the following is true? A. y = x 2. y =2x. x = y 2. x =2y c) enicia plans to sell the car when its value depreciates to $3000. If her car continues to depreciate according to enicia s estimate, what is the minimum number of years from the date of purchase that the car will have a value less than $3000? Show your work or explain how you found your answer. 27. Moore s Prediction In 975, researcher Gordon Moore made a prediction about the number of transistors on a computer chip. At that time, computer chips contained about 6,400 transistors. He predicted that the number of transistors on a computer chip would double every 2 years. 25. What is the value of log 3 27? A a) ased on Moore s prediction, how many transistors would be on a computer chip by the year 997? Write your answer in scientific notation. Show your work or explain how you found your answer. b) In 997, a manufacturer s premium computer chip had 7.5 million transistors. escribe whether Moore s prediction was accurate. Show your work or explain how you found your answer. page 5

6 28. arbon 4 is a common form of carbon which decays exponentially over time. The half-life of arbon 4, that is the amount of time it takes for half of any amount of arbon 4 to decay, is approximately 5730 years. Suppose we have a plant fossil and that the plant, at the time it died, contained 0 micrograms of arbon 4 (one microgram is equal to one millionth of a gram). 30. The population of a small town in North arolina is 4,000, and it has a growth rate of 3% per year. Which expression can be used to calculate the town s population x years from now? A. 3(4, 000) x. 4, 000(.03) x. 4, 000x.03. 4, 000x 3 a) Using this information, make a table to calculate how much arbon 4 remains in the fossilized plant after 5730 n years for n = 0,, 2, 3, 4. b) What can you conclude from the previous part. about when there is one microgram of arbon 4 remaining in the fossil? c) How much carbon remains in the fossilized plant after 2865 = years? Explain how you know. d) Using the information from the previous part, can you give a more precise response to when there is one microgram of arbon 4 remaining in the fossilized plant? 3. A patient is given a 00-milligram dosage of a drug that decays exponentially, with a half-life of 6 hours. Which equation could be used to find the milligrams of drug remaining (y) after x hours? A. y = 00(6) 0.5x. y = 00(x) 0.5/6 29. The number of bacteria in a sample doubles every four hours. At the end of 24 hours there are 30,720 bacteria present in a sample.. y = 00(0.5) x/6. y = 00(0.5x) /6 a) How many bacteria were present initially? Show your work. b) uring which four-hour period will 5 million bacteria first be present? Show your work. c) Write a mathematical expression to determine the number of bacteria present at the end of any four-hour period. page 6

7 Problem-Attic format version c_ EducAide Software Licensed for use by Ismael Hernandez Terms of Use at 05/20/ , 6250, 3, A A cubes are needed to build this tower. Tower 2 cubes high: 76 cubes 2n 2 n is a function used to calculate the number of cubes needed for a tower n cubes high. A