Algebra I Unit 7 Review. Unit 7 Review 1)A population of bacteria triples in size every day. a) Model the bacteria population with an exponential function.

Slides:

Advertisements

Similar presentations

CONTINUOUSLY COMPOUNDED INTEREST FORMULA amount at the end Principal (amount at start) annual interest rate (as a decimal) time (in years)

Advertisements

Exponential Functions

Models of Exponential and Log Functions Properties of Logarithms Solving Exponential and Log Functions Exponential Growth and Decay

4.1 Graph Exponential GrowthFunctions p. 228 What is an exponential function? What is exponential growth function? What is an asymptote? What information.

Exponential Functions and their Graphs

Exponential and Logarithmic Equations. Exponential Equations Exponential Equation: an equation where the exponent includes a variable. To solve, you take.

Unit 1 Test Review Answers

4.1 Exponential Growth Functions Retesting Opportunity: Dec Quiz: Dec. 3 Performance Exam: Dec. 4.

8-1: Exponential Growth day 2 Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions.

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 8-6 Exponential and Logarithmic Functions, Applications, and Models.

Exponential functions have a variable in the Exponent and a numerical base. Ex. Not to be confused with power functions which Have a variable base. Ex.

Holt Algebra Exponential Growth and Decay You should know how to solve these: Simplify each expression. 1. ( ) The first term of.

Homework Lesson Handout #5-27 (ODD) Exam ( ): 12/4.

Exponential Growth Exponential Decay Graph the exponential function given by Example Graph the exponential function given by Solution x y, or f(x)

MAT 150 Algebra Class #17. Objectives  Graph and apply exponential functions  Find horizontal asymptotes  Graph and apply exponential growth functions.

Solving Exponential Equations II LG: I can use trial and error to solve exponential equations.

PRECALCULUS I EXPONENTIAL FUNCTIONS Dr. Claude S. Moore Danville Community College.

8.2 – Properties of Exponential Functions

Section 4.1 Exponential Functions

Section 7.1: Graph Exponential Growth Functions Chapter 7: Exponential and Logarithmic Functions.

Exponential Functions

Journal: Write an exponential growth equation using the natural base with a horizontal asymptote of y=-2.

Chapter 8 Slide the Eraser. Question 1 write the following using exponents? 7 · 7 2 · 2 · 2 x · x · x· x · x· x · x.

Writing Exponential Growth Functions

Exponential Functions Section 5.1. Evaluate the exponential functions Find F(-1) Find H(-2) Find Find F(0) – H(1)

Exponential Graphs Equations where the variable (x) is the POWER y = ab x – h + k h moves the graph horizontally k moves the graph vertically.

$100 $200 $300 $400 $500 $200 $300 $400 $500 Exponents Scientific Notation Exponential Growth and Decay Properties of exponents Geometry Sequences.

Warm Up HW Check Jeopardy Exponents GraphsExponential Growth/Decay Compound Interest Random Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300.

Exponential Decay Functions 4.2 (M3) p Warm-Up Evaluate the expression without using a calculator. ANSWER –1 ANSWER –3 2.– ANSWER.

Chapter 8 Section 2 Properties of Exp. Functions

Algebra I Ch. 7 Warm-ups. Section 7-1 WU, Day 1 Graph the following systems of linear inequalities (sketch a graph on your paper) 1. y < ¼ x – 32. y

Exploring Exponential Models

EXAMPLE 3 Graph y = ab + k for 0 < b < 1 x – h Graph y = 3 –2. State the domain and range. 1 2 x+1 SOLUTION Begin by sketching the graph of y =, which.

8.2 Properties of Exponential Functions 8.3 Logarithmic Functions as Inverses.

Exponential Functions Chapter 10, Sections 1 and 6.

Objectives Use the number e to write and graph exponential functions representing real-world situations. Solve equations and problems involving e or natural.

Chapter 8: Exploring Exponential Models. What is an exponential equation? An exponential equation has the general form y=ab x.

How do we solve exponential and logarithmic equations and equalities?

Modeling Constant Rate of Growth (Rate of Decay) What is the difference between and An exponential function in x is a function that can be written in the.

6.2 Exponential Functions Objective: Classify an exponential function as representing exponential growth or exponential decay. Calculate the growth of.

Graph y = 3 x. Step 2: Graph the coordinates. Connect the points with a smooth curve. ALGEBRA 2 LESSON 8-1 Exploring Exponential Models 8-1 x3 x y –33.

Lesson 8.1.  Exponential Function: a function that involves the expression b x where the base b is a positive number other than 1.  Asymptote: a line.

HONORS ALGEBRA DAY 1: SOLVING EXPONENTIAL EQUATIONS & INEQUALITIES.

10.2 Exponential and Logarithmic Functions. Exponential Functions These functions model rapid growth or decay: # of users on the Internet 16 million (1995)

Drill If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by the.

Objectives: The student will be able to… 1)Graph exponential functions. 2)Solve exponential equations and inequalities.

Chapter Three Jeopardy. $200 $400 $600 $800 $1000 Exponential Graphs Logarithmic Graphs Properties of Logarithms Solving Equations Modeling.

ALGEBRA CHAPTER 8 TEST REVIEW. A)B) C)D) 1. Simplify the expression.

Section 8-2 Properties of Exponential Functions. Asymptote Is a line that a graph approaches as x or y increases in absolute value.

Chapter 9 Review.

Recall the compound interest formula A = P(1 + )nt, where A is the amount, P is the principal, r is the annual interest, n is the number of times the.

8.1 Exploring Exponential Models

Exponential Functions, Growth and Decay

1.3 Exponential Functions Day 2

8.1 Exploring Exponential Models

8-1 Exploring Exponential Models

1.3 Exponential Functions Day 1

Algebra I Chapter 8 Review

6.1 Exponential Growth and Decay Functions

MATH 1311 Section 4.1.

Exponential Equations Applications.

7.1 & Graphing Exponential Transformations

Section 5.1 – Exponential Functions

Algebra Exponentials Jeopardy

Introduction We exhibit many situations involving exponential growth of functions. For instance, the increase in the amounts of investment is a case.

6.1 Exponential Growth and Decay Functions

Notes Over 8.5 Exponential Growth

Warm-up: Exponent Laws

The number of bees in a hive is growing exponentially at a rate of 40% per day. The hive begins with 25 bees. Which function models the population of the.

Jeopardy Choose a category. Click to begin..

Presentation transcript:

Algebra I Unit 7 Review

Unit 7 Review 1)A population of bacteria triples in size every day. a) Model the bacteria population with an exponential function. b)If the initial population of the bacteria is 125 cells, what will the population be after 25 days?

1)A population of bacteria triples in size every 5 days. a) Model the bacteria population with an exponential function. b)If the initial population of the bacteria is 125 cells, what will the population be after 25 days? Unit 7 Review Answer 30,375 cells y = 125 · 3 x where x is the number days

Unit 7 Review

Answer = 25 1/2 = 27 1/3 = x 3/4

Unit 7 Review 3)Simplify using positive exponents. a) (x -2 y -4 ) -3 (y 7 y 3 ) b) (2x 5 ) 3 4 x -1 y 8 c) a 6 -3 a 7

Unit 7 Review 3)Simplify using positive exponents. a) (x -2 y -4 ) -3 (y 7 y 3 ) b) (2x 5 ) 3 4x -1 y 8 c) a 6 -3 a 7 Answer = x 6 y 12 y 10 = x 6 y 22 8x 15 x 2x 16 = 4y 8 y 8 a -18 a 21 a 3 = = = a -21 a 18

Unit 7 Review 4)Write an exponential function to model each situation (for x years). Find each amount after the specified time. a) $200 principal 5 years 4% compounded annually b) $3000 investment 3 years 8% loss each year

Unit 7 Review 4)Write an exponential function to model each situation (for x years). Find each amount after the specified time. a) $200 principal 5 years 4% compounded annually b) $3000 investment 3 years 8% loss each year Answer y = 200·1.04 x = $ y = 3000·0.92 x = $

Unit 7 Review 5)These graphs show functions in the form y = a(b) x. a.Which graph has b < 1? b.Which axis is an asymptote in Graph B? c.What is the value of a in Graph A?

5)These graphs show functions in the form y = a(b) x. a.Which graph has b < 1? b.Which axis is an asymptote in Graph B? c.What is the value of a in Graph A? Unit 7 Review Answer Graph B x-axis a = 2

Unit 7 Review 6)a) What is the half life of this substance? b) Estimate an exponential equation that models the graph.

Unit 7 Review 6)a) What is the half life of this substance? b) Estimate an exponential equation that models the graph. Answer ≈ 20 minutes y = 100·0.966 x y = 100·b x  50 = 100·b 20  0.5 = b 20  b = 20 th root of 0.5  b ≈ 0.966