MRS. PROFIO-MILLER'S MATH WEBSITE - Home



Math IMrs. Profio-MillerName: _______________________Unit 6: Exponential FunctionsDayA DayB DayTopicHomeworkHW Grade (1 stamp = ? completed, 2 stamps = all complete)1Tuesday, March 31stMonday, March 30thSequences: Arithmetic vs. GeometricPage 3 #1-112Thursday, April 2nd Wednesday, April 1st Sequences: Equations to Tables to GraphsPage 4-5 #12 - 133Tuesday, April 7th Wednesday, April 8thExponential GrowthQUIZPages 6 #14 – 19 4Thursday, April 9th (Mon 4/6 – teacher absent)Friday, April 10th Exponential DecayPages 7 #20 – 22 5Monday, April 13th Tuesday, April 14th ReviewReview SheetAttach Review Sheet (with work) for 2 extra credit points!6Wednesday, April 15th Thursday, April 16th TESTTurn in this packet for a HW grade!4431562150052-17018090805Need tutoring or to make up an assignment? Stay after school on Tuesdays and Thursdays from 2:30—3:45 pm!00Need tutoring or to make up an assignment? Stay after school on Tuesdays and Thursdays from 2:30—3:45 pm!-170180276860Need 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 # )00Need 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 # )-124460220980Notes and Assignments are on Mrs. P.M.’s website:profiomillermath.00Notes and Assignments are on Mrs. P.M.’s website:profiomillermath.Unit 6 StandardsSTANDARD 1: Compare Linear to Exponential FunctionsF-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functionsRecognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.STANDARD 2: Building Exponential FunctionsF-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. ★STANDARD 3: Interpret Exponential FunctionsInterpret expressions for functions in terms of the situation they model.F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Note: At this level, the focus is linear and exponential functions.F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Unit 6 Homework Day 1: 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? (circle one)What is the initial term? ________ What is the rate of change? ________ Is this a common ratio or common difference? (circle one)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? (circle one)What is the initial term? ________ What is the rate of change? ________ Is this a common ratio or common difference? (circle one)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? (circle one)What is the initial term? ________ What is the rate of change? ________ Is this a common ratio or common difference? (circle one)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? (circle one)What is the initial term? ________ What is the rate of change? ________ Is this a common ratio or common difference? (circle one)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, . . .492252030734000Unit 6 Day 2 Homework Killer Plants 12. 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.366776063500 Use the data to graph the situation. Be sure to label your axes and title your graph.Write a NOW-NEXT rule representing the situation.Write an explicit equation using y = . Explain what the variables in your equation 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?13. 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 What is the initial area covered? __________ What is the growth factor of area covered? ________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 3 Homework 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%.Whose mice are reproducing fastest? _______________Whose mice are reproducing slowest? _____________Compound Interest – Use the formula A = P(1 + r/n)nt for the problems below.16. If interest is compounded annually, find the compound amount of $1000 invested for 5 years at 9.5% interest.17. If interest is compounded semiannually at 10% per year, what would you need to invest to have $1000 at the end of 3 years?18. If interest is compounded monthly, find the compound amount of $1200 invested for four and a half years at 12%.19. 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 4: Exponential Decay20. Suppose a new golf ball drops downward from a height of 27 feet onto a paved parking lot and keeps bouncing up and down, again and again. Rebound height of the ball should be 2/3 of its drop height. Fill in the table of the rebound heights.Bounce #012345678910Rebound Height(in ft)27What rule relating NOW and NEXT shows how to calculate the rebound height for any bounce from the height of the preceding bounce?What rule beginning “y = …” shows how to calculate the rebound height after any number of bounces?Using your rule in part c.), what is the predicted height of the ball after 15 bounces?If the ball drops first from only 15 feet, how will the equation and graph change?21. You buy a vehicle for $8,500. It depreciates in value 8% every year. a.) What is the initial value? ___________b.) What is the decay rate? ____________c.) What is the decay factor? ______________d.) Write an equation representing the situation using t = time in years, and v(t) = value of your vehicle.__________________________________e.) What is the predicted value of your vehicle after it is 10 years old? _______________________22. 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? ______________________ 6 years? ___________________________ ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download