Name Score Algebra 1B Assignments Eponential Functions (All graphs must be drawn on graph paper!) 8-6 Pages 463-465: #1-17 odd, 35, 37-40, 43, 45-47, 50, 51, 54, 55-61 odd 8-7 Pages 470-473: #1-11 odd, 12-22, 24, 25, 29, 33, 38, 40, 57-61 odd 8-8a Pages 479-482: #3-10, 16-19, 33-39, 43, 57, 58, 60 8-8b Pages 479-482: #20-32, 40, 41, 44-49, 52, 56, 62 Quiz 8-6 to 8-8 Worksheet: Review of Functions and Graphs 10-8 Pages 601-604: #2, 3, 5, 6, 8, 10-14, 16, 30-33, 43-47 odd Review Test Worksheet: Eponential Functions Review Eponential Functions
Warm Up: Simplif each epression. 1. 3 2 2. Section 8-6 2 5 4 3. 3 0 a b c 7 2 Use inductive reasoning to find the net two numbers in each pattern. 4. 5, 8, 11, 14, 5. 19, 17, 15, 13, 6. 1, 3, 9, 27, 7. 400, 200, 100, 50, Objective: To differentiate between arithmetic and geometric sequences To form geometric sequences arithmetic sequence: A number pattern formed b adding a fied number to each previous term. 1, 3, 5, 7, 9, (common difference) (What tpe of graph does this make?) geometric sequence: A number pattern formed b multipling a fied number to each previous term. 1, 2, 4, 8, 16, (common ratio) (What tpe of graph does this make?)
Eample #1: Determine whether each sequence is arithmetic, geometric, or neither. State the common difference or ratio, if applicable. a) 25, 5, 1, 1, b) 5, 1, -3, -7, c) 1, 2, 4, 7, 11, 5 Eample #2: Find the common ratio and the net two terms of each sequence. a) 3, -15, 75, -375, b) 90, 30, 10, 10 3, Closure Question: Eplain the difference between an arithmetic and geometric sequence.
Section 8-7 Warm Up: Graph each function. 1. 3 4 2. 2 1 Simplif each epression without a calculator. 3. 3 5 4. 2 10 3 5. 7 2 1 6. 4 3 2 Objective: To evaluate and graph eponential functions eponential function: ab evaluate: plug in a value for and solve for domain: all possible -values range: all possible -values Eample #1: Evaluate each function. a) 4 for 2, 0, 3 b) ( ) 2 3 f for the domain 1, 0, 2
Eample #2: a) Suppose 10 rabbits are taken to an island. The rabbit population then triples ever ear. Use an eponential function to find out how man rabbits there would be after 12 ears. b) Suppose two mice live in a barn. If the number of mice quadruples ever 3 months, use an eponential function to find out how man mice will be in the barn after 2 ears. Steps to graph eponential functions: Make a table of values with 5 points ( = -2, -1, 0, 1, 2) Plot the points Connect the points to form a smooth curve Eample #3: Graph each function without a calculator. State the domain and range. a) 5 b) 3 2 Eample #4: The function f ( ) 1.5 models the increase in size of an image being copied over and over at 150% on a photocopier. Graph the function. Closure Question: 4 Is the equation an eponential function? Eplain our answer.
Warm Up: Eponential growth and deca eploration Section 8-8a Objective: To model eponential growth Eplanation of Eponential Growth: Start with 20 bacteria and grow at a rate of 30% per ear. What is the growth factor? ear 1 = ear 2 = ear 3 = ear 4 = Eponential Growth: ab (eamples: bacteria, population, interest) Use the eponential rule for the bacteria problem above. Do ou get the same answer? Eample #1: In 1998 a town had a population of 13,000 people. Since 1998 the population increased 4% per ear. a) Write an equation to model this situation. b) Estimate the population in 2006.
Eample #2: a) Suppose ou deposit $1000 in a college fund that pas 7.2% interest compounded annuall. What is the balance after 5 ears? b) Suppose ou deposit $1000 in a college fund that pas 7.2% interest compounded quarterl. What is the balance after 5 ears? Eample #3: Calculate the balance in a bank account with $3000 principal earning 3.6% compounded monthl for 2 ears. Closure Question: Would ou rather have $600 in an account paing 5% interest compounded annuall or $500 in an account paing 6% compounded quarterl? Eplain our answer.
Section 8-8b Warm Up: Graph each function using the table of values 2, 1,0,1, 2 1. 2 4 2. 1 3 2 without a calculator. Suppose ou deposit $1500 in an account paing 3.5% interest for 6 ears. 3. Find the account balance if the mone is compounded annuall. 4. Find the account balance if the mone is compounded quarterl. Objective: To model eponential deca Eample #1: The half-life of a radioactive substance is the length of time it takes for one half of the substance to deca into another substance. To treat some forms of cancer, doctors use radioactive iodine. The half-life of iodine-131 is 9 das. A patient receives a 32-mCi (millicuries, a measure of radiation) treatment. How much iodine-131 is left in the patient 27 das later?
Eponential Deca: ab (eamples: radioactive deca, endangered species, car value) Use the eponential rule for the radioactive deca problem in eample #1. Eample #2: The population of an endangered species of animals has decreased 2.4% each ear. There were 60 of these animals in 1998. a) Write an equation to model this situation. b) Estimate how man animals remained in 2005. Eample #3: You bu a used truck for $14,000. It depreciates at a rate of 15% per ear. Find the value of the truck after 6 ears. Closure Question: Eplain the difference between an eponential growth function and an eponential deca function.
Section 10-8 Warm Up: Write an equation for each function. 1. A linear function that passes through the points (0, 4) and (6, 1). 2. An eponential function that passes through the points (0, 5) and (1, 15). Graph each function using the table of values 1, 2,3, 4. 3. 2 1 4. 1 3 Objective: To choose a linear or eponential model for data Eample #1: Calculate the average rate of change for warm-up problems 3 and 4. Use the -values from 1 2, 1 3, and 1 4. What do ou notice about the average rate of change for linear functions versus eponential functions?
How do ou decide which model best fits the data? 1) Graph the function 2) Analze the data a) Linear ( m b ) Has a common difference (subtract values) b) Eponential ( ab ) Has a common ratio (divide values) Eample #2: Graph each set of points. Which model is most appropriate for each set? a) (-2, 1), (0, 2), (1, 4), (2, 7) b) (-2, -2), (0, 2), (1, 4), (2, 6) Eample #3: Analze the data to determine which kind of function best models the data in each table. Then write an equation to model the data. a) b) 0 1 1 1.5 2 2 3 2.5 4 3 0 4 1 4.4 2 4.84 3 5.324 4 5.8564
Since real-life data is not alwas eact, ou ma need to find the best possible model. Eample #4: Suppose ou are studing frogs that live in a nearb wetland area. The data below were collected b a local conservation organization. The indicate that number of frogs estimated to be living in the wetland area over a five-ear period. a) Determine which kind of function best models the data. Estimated Year Population 0 120 1 101 2 86 3 72 4 60 b) Write an equation to model the data. Eample #5: The table below shows the population of a town in South Dakota. Let = 0 correspond to the ear 1980. a) Determine which kind of function best models the data. Year Population 0 7300 5 7575 10 7875 15 8200 20 8500 b) Write an equation to model the data. Closure Question: Eplain how ou choose a linear or eponential model for data?