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Algebra 1 Unit 4 Exponential Functions Notes,MGSE9 12 A CED 1. Create equations and inequalities in one variable and use them to solve problems Include equations arising from exponential functions. integer inputs only,MGSE9 12 A CED 2, Create exponential equations in two or more variables to represent relationships between quantities graph equations on coordinate axes. with labels and scales The phrase in two or more variables refers to formulas like the compound interest formula in which. A P 1 r n nt has multiple variables, Build a function that models a relationship between two quantities. MGSE9 12 F BF 1, Write a function that describes a relationship between two quantities. MGSE9 12 F BF 1a, Determine an explicit expression and the recursive process steps for calculation from context For example if Jimmy starts out with 15.
and earns 2 a day the explicit expression 2x 15 can be described recursively either in writing or verbally as to find out how much. money Jimmy will have tomorrow you add 2 to his total today Jn Jn 1 2 J0 15. MGSE9 12 F BF 2, Write geometric sequences recursively and explicitly use them to model situations and translate between the two forms Connect. geometric sequences to exponential functions,Build new functions from existing functions. MGSE9 12 F BF 3, Identify the effect on the graph of replacing f x by f x k k f x f kx and f x k for specific values of k both positive and negative find. the value of k given the graphs Experiment with cases and illustrate an explanation of the effects on the graph using technology Focus. on vertical translations of graphs of linear and exponential functions Relate the vertical translation of a linear function to its y intercept. Understand the concept of a function and use function notation. MGSE9 12 F IF 1, Understand that a function from one set the input called the domain to another set the output called the range assigns to each. element of the domain exactly one element of the range i e each input value maps to exactly one output value If f is a function x is the. input an element of the domain and f x is the output an element of the range Graphically the graph is y f x. MGSE9 12 F IF 2, Use function notation evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a.
MGSE9 12 F IF 3, Recognize that sequences are functions sometimes defined recursively whose domain is a subset of the integers Generally the scope of. high school math defines this subset as the set of natural numbers 1 2 3 4 By graphing or calculating terms students should be able to. show how the recursive sequence a1 7 an an 1 2 the sequence sn 2 n 1 7 and the function f x 2x 5 when x is a natural number. all define the same sequence, Interpret functions that arise in applications in terms of the context. MGSE9 12 F IF 4, Using tables graphs and verbal descriptions interpret the key characteristics of a function which models the relationship between two. quantities Sketch a graph showing key features including intercepts interval where the function is increasing decreasing positive or. negative relative maximums and minimums symmetries end behavior. MGSE9 12 F IF 5, Relate the domain of a function to its graph and where applicable to the quantitative relationship it describes For example if the. function h n gives the number of person hours it takes to assemble n engines in a factory then the positive integers would be an. appropriate domain for the function,MGSE9 12 F IF 6.
Calculate and interpret the average rate of change of a function presented symbolically or as a table over a specified interval Estimate. the rate of change from a graph,Analyze functions using different representations. MGSE9 12 F IF 7, Graph functions expressed algebraically and show key features of the graph both by hand and by using technology. MGSE9 12 F IF 7e, Graph exponential functions showing intercepts and end behavior. MGSE9 12 F IF 9, Compare properties of two functions each represented in a different way algebraically graphically numerically in tables or by verbal. descriptions For example given a graph of one function and an algebraic expression for another say which has the larger maximum. Algebra 1 Unit 4 Exponential Functions Notes,Unit 4 Exponential Functions.
After completion of this unit you will be able to Table of Contents. Lesson Page,Learning Target 1 Graphs of Exponential Functions. Day 1 Graphing Exponential,Evaluate an exponential function Functions 4. Graph an exponential function using a xy chart,Day 2 Applications of. Exponentials Growth Decay 8, Learning Target 2 Applications of Exponential Functions. Create an exponential growth and decay function,Day 3 Applications of.
Evaluate the growth decay function,Exponential Functions 10. Create a compound interest function,Compound Interest. Evaluate a compound interest function,Solve an exponential equation. Day 4 Explicit Sequences,Geometric Arithmetic 12,Learning Target 3 Sequences. Create an arithmetic sequence, Create a geometric sequence Day 5 Recursive Sequences.
Geometric Arithmetic 14,Timeline for Unit 4,Monday Tuesday Wednesday Thursday Friday. October 28th 29th 30th 31st November 1st,Day 1 Graphing Day 2 Day 3. Exponential Applications of Applications of,Functions Exponentials Exponential. Growth Functions,Decay Compound,4th 5th 6th 7th 8th. Day 4 Explicit No School Day 5 Recursive Unit 4 Review Unit 4 Test. Sequences Teacher Work Day Sequences,Geometric Geometric.
Arithmetic Arithmetic,Algebra 1 Unit 4 Exponential Functions Notes. Day 1 Exponential Functions,Standard s MGSE9 12 A CED 2. Create exponential equations in two or more variables to represent relationships between. quantities graph equations on coordinate axes with labels and scales. Exploring Exponential Functions, Which of the options below will make you the most money after 15 days. a Earning 1 a day,x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. b Earning a penny at the end of the first day earning two pennies at the end of the second day earning 4. pennies at the end of the third day earning 8 pennies at the end of the fourth day and so on. x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15,The general form of an exponential function is.
a represents your start initial value y intercept,b represents your change. Variable is in the exponent versus the base,Start small and increase quickly or vice versa. Asymptotes graph heads towards a horizontal line but. never touches it, Constant Ratios multiply by same number every time. Evaluating Exponential Functions, For exponential functions the variable is in the exponent but you still evaluate by plugging in the value given. Example 1 Evaluate each exponential function, a f x 2 3 x when x 5 b y 8 0 75 x when x 3 c f x 4x find f 2.
Algebra 1 Unit 4 Exponential Functions Notes,Graphing Exponential Functions. The general form of an exponential function is,Where a represents your starting or initial value. b represents your growth decay factor change, An asymptote is a line that an exponential graph gets closer and closer to but never touches or crosses. The equation for the line of an asymptote is always y. Graph the following,Growth or decay 1 8 6 4 2 2 4 6 8. Asymptote 2,Y intercept 4,Growth or decay,1 8 6 4 2 2 4 6 8.
Y intercept,Algebra 1 Unit 4 Exponential Functions Notes. Creating Exponential Functions, Exponential Functions a Start initial amount y int. b Change growth decay,x How often change occurs,y abx y Result of change over time. Write the equations that model these exponential functions. 5 March Madness is an example of exponential decay At each round of the tournament only the winning. teams stay so the number of teams playing at each round is half of the number of teams playing in the. previous round If 64 teams are a part of the official bracket at the start how many teams are left after 5 rounds. 6 Bacteria have the ability to multiply at an alarming rate where each bacteria splits into two new cells. doubling the number of bacteria present If there are ten bacteria on your desk and they double every hour. how many bacteria will be present tomorrow desk uncleaned. 7 Phosphorus 32 is used to study a plant s use of fertilizer It has a half life of 14 days Write the exponential. decay function for a 50 mg sample Find the amount of phosphorus 32 remaining after 84 days. Algebra 1 Unit 4 Exponential Functions Notes,Algebra 1 Unit 4 Exponential Functions Notes. Day 2 Applications of Exponential Functions Growth Decay. Standard s MGSE9 12 A CED 2, Create exponential equations in two or more variables to represent relationships between quantities graph.
equations on coordinate axes with labels and scales. Review of Percentages Remember percentages are always out of 100. To change from a percent to a decimal, Option 1 Divide by 100 Option 2 Move the decimal two places to the. 25 6 5 2 10 3 05,Exponential Growth and Decay, Can you tell whether these functions represent growth or decay. A y 8 4 x B f x 2 5 7 x C h x 0 2 1 4 x D y 0 99 x E y 1 01 x. When we discuss exponential growth and decay we are going to use a slightly different equation than y abx. Exponential Growth Exponential Decay, A quantity increases over time A quantity decreases over time. y a 1 r t y a 1 r t,where a 0 where a 0,y final amount y final amount. a initial amount a initial amount, r growth rate express as decimal r decay rate express as decimal.
t time t time, 1 r represents the growth factor 1 r represents the decay factor. Finding Growth and Decay Rates, Identify the following equations as growth or decay Then identify the initial amount growth decay factor and. the growth decay percent, a y 3 5 1 03 t b f t 10 000 0 95 t c y 2 500 1 2 t. Growth Decay growth Growth Decay Growth Decay,Initial Amount 3 5 Initial Amount Initial Amount. Growth Decay Factor 1 03 Growth Decay Factor Growth Decay Factor. Growth Decay 0 03 3 Growth Decay Growth Decay,Algebra 1 Unit 4 Exponential Functions Notes.
Growth and Decay Word Problems, Example 1 The original value of a painting is 1400 and the value increases by 9 each year Write an. exponential growth function to model this situation Then find the value of the painting in 25 years. Growth or Decay,Starting value a,Rate as a decimal. Example 2 The cost of tuition at a college is 15 000 and is increasing at a rate of 6 per year Find the cost of. tuition after 4 years,Growth or Decay,Starting value a. Rate as a decimal, Example 3 The value of a car is 18 000 and is depreciating at a rate of 12 per year How much will your car. be worth after 10 years,Growth or Decay,Starting value a.
Rate as a decimal, Example 4 A bungee jumper jumps from a bridge The diagram shows the bungee jumper s height above the. ground at the top of each bounce What is the bungee jumper s height at the top of the 5 th bounce. Growth or Decay,Starting Value,Rate as a decimal,Algebra 1 Unit 4 Exponential Functions Notes. Day 3 Applications of Exponential Functions Compound Interest. Standard s MGSE9 12 A CED 2, Create exponential equations in two or more variables to represent relationships between quantities graph. equations on coordinate axes with labels and scales. In middle school you learned about simple interest which is interest that is only earned on the original amount. of money called the principal It s formula is I Prt where P represents principal r represents rate t represents. time and I represents interest, Compound Interest is interest earned or paid on both the original amount principal and previously earned. Compound Interest,A balance after t years,P Principal original amount.
r interest rate as a decimal,n number of times interest is compounded per year. t time in years, Example 1 Write a compound interest function that models an investment of 1000 at a rate of 3. compounded quarterly Then find the balance after 5 years. Example 2 Write a compound interest function that models an investment of 18 000 at a rate of 4 5. compounded annually Then find the balance after 6 years. Example 3 Write a compound interest function that models an investment of 4 000 at a rate of 2 5. compounded monthly Then find the balance after 10 years. Algebra 1 Unit 4 Exponential Functions Notes,Solving Exponential Equations. An exponential equation is an equation containing one or more expressions that have a variable as an. exponent When solving exponential equations you want to rewrite the equations so they have the same. bases If they have the same bases you set the exponents equal to each other. If bx by then x y,Solve 2x 4 2 x 10 Explanation,Solve the following equations. a 33x 7 3x 1 b 2,c 22x 6 4 d 54x 1 125,Algebra 1 Unit 4 Exponential Functions Notes.
Day 4 Arithmetic and Geometric Sequences Explicit Formulas. Standard s, MGSE9 12 F BF 2 Write geometric sequences recursively and explicitly use them to model situations and. translate between the two forms Connect geometric sequences to exponential functions. MGSE9 12 F BF 1a Determine an explicit expression and the recursive process steps for calculation from. A sequence is a list of numbers or objects called terms in a certain order. Arithmetic Sequences, The difference between any two terms is always the same. Algebra 1 Unit 4 Exponential Functions Notes 1 Name Block Teacher Algebra 1 Unit 4 Notes Modeling and Analyzing Exponential Functions DISCLAIMER We will be using this note packet for Unit 4 You will be responsible for bringing this packet to class EVERYDAY If you lose it you will have to print another one yourself An electronic copy of this packet can be found