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Common Core IMrs. Profio-MillerName: _______________________Unit 6: Exponential FunctionsDayA DayB DayTopicHomeworkStamp1Tues., February 11Mon., February 17Rules of Exponents: zero, negative, fractionalPage 2-32Rules of Exponents: product, power, quotientPage 4-53Tuesday, February 18Wed., February 19Sequences: Arithmetic vs. GeometricPage 64Thurs., February 20Friday, February 21Sequences: Equations to Tables to GraphsTranslationsPage 7-85Mon., February 24Tuesday, February 25Exponential GrowthPages 96Wed., February 26Thursday, February 27Exponential DecayPages 107Friday, February 28Monday, March 3ReviewPage 11-138Tuesday, March 4Wednesday, March 5TESTTurn in this packet for a HW grade!4431562150052Need tutoring or to make up an assignment? Stay after school on Tuesdays and Wednesdays from 2:30—3:30 pm!Need some online help? Go to SAS Curriculum Pathways (login: BroughtonStudent) Use the Quick Launch numbers 5061 – 5064 (to access these, type in the top right of the homepage where it says QL # )Unit 6 Day 1 HOMEWORKI. Short Answer:1. What is the “job” of an exponent? ____________________________________________2. Any nonzero number raised to the ZERO power will always equal __________.3. If a number has a negative exponent, we will ______________ the base and make the power positive.4. Label the base and the exponent:km5. Label the index, the radical, and the radicand: wsII. Write each of the following calculations in a more compact form by using exponents:1. 5 5 5 52. (3w) (3w) (3w) (3w) (3w)3. 8 p p pIII. Write each in an expanded form (i.e. there should be NO exponents written in your answer):1. 7x2y42. (2eg)33. 9(w5y) IV. Simplify each expression:1. 3602. 14412 3. 42 4. 823 5. 4 20 V. Write each as an exponential: 1. p 2. 3t 3. 6x5VI. Write each as radical:1. x12 2. y15 3. z23VII. Rewrite each so there are no negative exponents and simplify:1. x3y22. x5y-1 3. x-4yw-2 VIII. Write an exponential expression that fits this description and then evaluate:1. the base is 4 with an exponent of 32. the base is 7 with an exponent of 23. the base is 2 with an exponent of 5IX. Write a radical expression that fits this description and then evaluate:1. the index is 2 and the radicand is 252. the index is 3 and the radicand is 7293. the index is 5, the radicand is 32 with an exponent of 3 X. Simplify the expression – write final answer in scientific notation:1. (4.5 x 109) (1.6 x 102) 2. (4 x 103) (9 x 107) XI. Write your final answer for each problem below in scientific notation:1. The speed of light in space is 3 x 105 km per second. It takes light 5 x 102 seconds to travel from the sun to the earth. How many kilometers away is the sun?2. The human body contains about 3.2 x 102 liters of blood for each pound of body weight. Each liter of blood contains about 5 x 1012 red blood cells. About how many red blood cells are in the body of a 100-pound person? Unit 6 Day 2 HomeworkI. Match the rule written in symbols (#1 – 5) with the rule written in words (A E): _____1. bm bn = bm + nA. to eliminate a negative power, shift the base and write it with a positive power _____2. (bm)n = b m nB. when you divide like bases, keep the base and subtract the powers_____3. bmbn = bm nC. when you raise a power to a power, keep the base and multiply the powers _____4. b0 = 1D. an nonzero number raised to the zero power equals one_____5. bm = 1bmE. when you multiply like bases, keep the base and add the powers_____6. (ab)m = am bmF. when you raise a product to a power, share the power with each base II. Simplify each expression:1. x5 x4 x2. (y5)7 3. (2x4y3)34. k8k35. 18y5(3y2)2 6. 60 7. x4 y8 8. x3 y-5x-8 y8 9. 33xy9-3xy3 10. 20x4y10z35x9y10z211. m3 (m2)4III. Name the value that should replace the question mark(s) to create a true statement: 1. W 5 W ? = W 252. ( ? X? Y? ) 2 = 9 X4 Y83. ? 0 = 14. A? B7 = B7A25. 36 x9 y?-12 x? y10 = -3x7y5IV. Find the area of each:1. Rectangle whose length is: 9x2 and whose width is: 6x42. Square whose side lengths are: 8x3y73. Triangle whose base is: 14k5 and whose height is: 3kV. Find the volume of the cube whose side lengths are: 3xy8Now, find the area of the top surface of the cube.VI. Find the volume of the rectangular prism whose length is: 2a6b2c whose width is: abc4 whose height is: 3b7cNow, find the area of the shaded side of the box.VII. Find and correct the errors:1. 4x2 3x5 = 7x72. (3y2) (2y4) = 6y83. c2 c7 = c5Unit 6 Homework Day 3: Arithmetic and Geometric SequencesYou visit the Grand Canyon and drop a penny off the edge of a cliff.? The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on.? What is the total distance the object will fall in 6 seconds? ______________Is this sequence arithmetic or geometric?What is the initial term? ________ What is the rate of change (common ratio or common difference)? ________Write a NOW-NEXT rule: _________________________ The sum of the interior angles of a triangle is 180?, of a quadrilateral is 360? and of a pentagon is 540?.? Assuming this pattern continues, find the sum of the interior angles of a dodecagon (12 sides). ___________Is this sequence arithmetic or geometric?What is the initial term? ________ What is the rate of change (common ratio or common difference)? ________Write a NOW-NEXT rule: _________________________ After knee surgery, your trainer tells you to return to your jogging program slowly.? He suggests jogging for 12 minutes each day for the first week.? Each week thereafter, he suggests that you increase that time by 6 minutes per day.? How many weeks will it be before you are up to jogging 60 minutes per day? __________Is this sequence arithmetic or geometric?What is the initial term? ________ What is the rate of change (common ratio or common difference)? ________Write a NOW-NEXT rule: _________________________You complain that the hot tub in your hotel suite is not hot enough.? The hotel tells you that they will increase the temperature by 10% each hour.? If the current temperature of the hot tub is 75? F, what will be the temperature of the hot tub after 3 hours, to the nearest tenth of a degree? _____________________Is this sequence arithmetic or geometric?What is the initial term? ________ What is the rate of change (common ratio or common difference)? ________Write a NOW-NEXT rule: _________________________5. A culture of bacteria doubles every 2 hours.? If there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours? __________________Is this sequence arithmetic or geometric?What is the initial term? ________ What is the rate of change (common ratio or common difference)? ________Write a NOW-NEXT rule: _________________________Determine if the sequence is geometric, arithmetic or neither. If it is geometric or arithmetic, find the common ratio or common difference.6. -1, 6, -36, 216, . .7. 4, 16, 36, 64, . . .8. -2, -4, -8, -16, . . .9. 7, 4, 1, -1, . . .10. 375, 75, 15, 3, 1/3, . . .11. -125, -107, -89, -71, . . .3836035307340Unit 6 Day 4 Homework Killer Plants Ghost Lake is a popular site for fishermen, campers, and boaters. In recent years, a certain water plant has been growing on the late at an alarming rate. The surface area of Ghost Lake is 25,000,000 square feet. At present, 1,000 square feet are covered by the plant. The Department of Natural Resources estimates that the area is growing by a scale factor of 1.5 every month.Number of Months12345Area Covered in Square Feet1,000 Complete the table below.Use the data to graph the situation. Be sure to label your axes and title your graph.404876038735Write 2 equations ( a recursive equation using NOW-NEXT and an explicit equation using y =) to represent the growth pattern of the plant on Ghost Lake.Explain what information the variables and numbers in your equations represent.How much of the lake’s surface will be covered with the water plant by the end of a year?In how many months will the plant completely cover the surface of the lake?Loon Lake has a “killer plant” problem similar to Ghost Lake. Using the table below, answer the following questions. Number of Years12345Area Covered in Square Feet5,00010,00020,00040,00080,000 Graph the data on the graph below. Be sure to label your axes and title your graph.403796543815 What is the initial area covered? __________What is the growth factor of area covered? ________How do you know that this situation is modeled by an exponential function?Write 2 equations ( a recursive equation using NOW-NEXT and an explicit equation using y =) to represent the growth pattern of the plant on Loon Lake.How much of the lake’s surface will be covered with the plant by the end of 7 years?The surface area of the lake is approximately 200,000 square feet. How long will it take before the lake is completely covered?Adapted from Growing, Growing, Growing Exponential Relationships, Connected Mathematics 2, Pearson, 2009.Unit 6 Day 5 HomeworkWrite a NOW-NEXT equation and explicit equation in function notation to assist in solving the following problems.Omar made the following calculation to predict the value of his baseball card collection several years from now:01301139.12148.843159.264170.40What is the initial value?____________ growth rate? _____________ growth factor?____________Write the equation for this problem.If the value continues to increase at this rate, how much would the collection be worth in three more years?Carlos, Latanya, and Mila work in a biology laboratory. Each of them is responsible for a population of mice. The growth factor for Carlos’s population of mice is 8/7. The growth factor for Latanya’s population of mice is 3. The growth factor for Mila’s population of mice is 125%.How mice are reproducing fastest?Whose mice are reproducing slowest?Compound Interest3. If interest is compounded annually, find the compound amount of $1000 invested for 5 years at 9.5% interest.4. If interest is compounded semiannually at 10% per year, what would you need to invest to have $1000 at the end of 3 years?5. If interest is compounded monthly, find the compound amount of $1200 invested for four and a half years at 12%.6. Suppose you invest $3000 at 15% annual interest. Calculate the amount you would have after one year if interest is compounded (a) quarterly, and (b) monthly.7. CHALLENGE: One hundred dollars is deposited in a bank which compounds interest quarterly yields $115 at the end of a year. What is the annual rate of interest?Unit 6 Day 6: Exponential Decay2952753238502.3. A radioactive isotype half-life every 18 months. If a sample begins at 6542, write an equation representing the situation. How many is there at 36 months? 45 months? 6 years? Exponential Functions Unit Review Records at the Universal Video store show that sales of new DVDS are greatest in the first month after the release date. Sales usually decrease by one-half every 3 months. Universal video sells 31886460 copies of one particular DVD after its release.What NOW-NEXT(recursive) rule predict the sales of this DVD in the following months?Write a “y = ” (explicit) rule. Define what x and y represent.How many copies are likely to be sold in the third month (the first half life period)? Given this situation and your rule in part b.), what is the value of x ?Predict how many DVDs are in the 12th month.In what month are sales likely to first be fewer than 5 copies?A man invests $10,000 in an account that pays 8.5% interest per year, what is the amount of money that he will have after 3 years if interest is… (use the formula where A= total amount, P=principle amount, r = rate, k =number of times compounded per year, and t = time in years. Compounded annually?Compounded quarterly?Compounded monthly?Find the next three terms in each sequence. Identify each as arithmetic, geometric, or neither. For each arithmetic or geometric sequence, find the common difference or common ratio. Then write a NOW-NEXT rule to describe the sequence.14, 11, 8, 5, 2 . . .______________________________________________3,000, 300, 30, 3 . . .______________________________________________5, 6, 8, 11, 15, 20 . . .______________________________________________Tell whether each situation produces an arithmetic sequence, a geometric sequence, or neither.The temperature rises at the rate of 0.75F per hour. ______________________A person loses 2 lbs each month. ______________________________________A toadstool doubles in size each week. _________________________________A person receives a 6% raise each year. _________________________________Graph each function on your calculator and state the y-intercept.Y = 2x – 3b. y = 3x + 1c. y = (1/3)xFor each of the following rules, decide whether the function represented is an example of: an increasing linear function, a decreasing linear function, an exponential growth function, an exponential decay function, or neither a linear or exponential function.Y = 5(0.4x)b. NEXT = 5 NOWY = 5 – 0.4xd. NEXT = NOW – 5Y = 5/xf. NEXT = 0.4 NOWIn 2000, the number of people worldwide living with HIV/AIDS was estimated at more than 36 million. That number was growing at an annual rate of about 15%.Make a table showing the projected number of people around the world living with HIV/AIDS in each of the ten years after 2000, assuming the growth rate remains 15% per year.Years after 2000012345678910AIDS Cases (in millions)Write two different kinds of rules that could be used to estimate the number of people living with HIV/AIDS at any time in the future.NEXT = ___________________________________________________________Y = ______________________________________________________________Use the rules from part b to estimate the number of people living with HIV/AIDS in 2015.What factors might make the estimate of part c an inaccurate forecast?Write each of the following expressions in a simpler equivalent exponential form.a. 74 79 = ____________b. x x4 = _________c. (x2)3 = ______________d. (2t3)4 = __________e. (5x3y4)(4x2y) = ________f. (c5d3)2 = _________g. (25)3 = _____________h. 13-3 = _________ i. 5755= _________j. t5t2= ________ k. 30x3y26xy= ______l. ab2a4b= ______m. = ________ n. 4x-2y-5x32= ________ 9. Write the following in exponential form:a. b. 10. Write the following in radical form:a. b. c. Evaluate part b.11. The graphs, tables, and rules below model four exponential growth and decay situations. For each graph, there is a matching table and a matching rule. Use what you know about the patterns of exponential relations to match each graph with its corresponding table and rule. In each case, explain the clues that can be used to match the items without any use of a graphing calculator or computer.34353585725 ................
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