Warmup 11-16 Simplify: 2. Simplify: Simplify :.

Slides:

Advertisements

Similar presentations

Unit 9. Unit 9: Exponential and Logarithmic Functions and Applications.

Advertisements

Growth and Decay Exponential Models. Differs from polynomial functions. Polynomial Functions have exponents of whole numbers Exponential Functions have.

Exponential Functions

Objective: Students will be able to write and evaluate exponential expressions to model growth and decay situations.

Precalc. 2. Simplify 3. Simplify 4. Simplify.

Partner practice Chapter 8 Review WHITEBOA RD. Chapter 8 Review DRAW -The basic shape of the graph of a linear equation -The basic shape of the graph.

Exponential & Logarithmic Functions

7-6 & 7-7 Exponential Functions

Chapter 8 Review. Rewrite into logarithm form: 1. 2.

Exponential Functions. Exponential Function f(x) = a x for any positive number a other than one.

1. 2 Switching From Exp and Log Forms Solving Log Equations Properties of Logarithms Solving Exp Equations Growth and Decay Problems

Exponential and Logarithmic Functions

LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”

Section 4.1 Logarithms and their Properties. Suppose you have $100 in an account paying 5% compounded annually. –Create an equation for the balance B.

Exponential Functions. Exponential Functions and Their Graphs.

Section 4.1 Exponential Functions

Test on Topic 16 Radicals Solutions

Notes Over 8.4 Rewriting Logarithmic Equations Rewrite the equation in exponential form.

7.3 Notes – Use Functions Involving e. A number that occurs frequently in nature is one that results when n gets infinitely large in the expression. As.

Chapter 8 Test Review Exponents and Exponential Functions

Exponential Functions

Sect 8.1 To model exponential growth and decay Section 8.2 To use e as a base and to apply the continuously and compounded interest formulas.

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

8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.

7.1 Exponential Models Honors Algebra II. Exponential Growth: Graph.

EQ: How do exponential functions behave and why?.

THE NATURAL BASE EXAMPLE 1 Simplify natural base expressions Simplify the expression. a.e2e2 e5e5 = e = e7e7 b. 12e4e4 3e3e3 = e 4 – 3 4 = 4e4e.

Objective Write and evaluate exponential expressions to model growth and decay situations.

Real Exponents Chapter 11 Section 1. 2 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Scientific Notation A number is in scientific notation when it is.

Exponential and Logarithmic Functions Chapter 11.

Warm-up: Exponent Laws Use exponent Laws to simplify each of the following: a) x 3 x 2 b) y 2 y -4 c) (d 5 ) -2 d) e) f)

Notes Over 7.1 no real 4th roots Finding nth Roots

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.

Section 9.3 We have previously worked with exponential expressions, where the exponent was a rational number The expression b x can actually be defined.

6.6 The Natural Base, e Warm-up Learning Objective: To evaluate natural exponential and natural logarithmic functions and to model exponential growth and.

3.1 (part 2) Compound Interest & e Functions I.. Compound Interest: A = P ( 1 + r / n ) nt A = Account balance after time has passed. P = Principal: $

Review of Chapter 8. Graphing Exponential Functions: Make and table and graph the function for the domain {0, 1, 2, 3} Plug in 0, 1, 2, and 3 in for x.

Final Jeopardy Question Exponents EVIL Exponents

Notes Over 5.2 Rewriting Logarithmic Equations and Rewrite the equation in exponential form. are equivalent. Evaluate each logarithm.

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

9x – 7i > 3(3x – 7u) 9x – 7i > 9x – 21u – 7i > – 21u

Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.

GrowthDecay. 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.

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

Section 3.1 Exponential Functions. Definition An exponential function is in the form where and.

3.2 Logarithmic Functions 2015 Digital Lesson. 3.1 Warm-up Mr. Smith deposited $6,500 in an account that pays the account pays 4.5% interest, compounded.

7.1 E XPONENTIAL F UNCTIONS, G ROWTH, AND D ECAY Warm Up Evaluate (1.08) (1 – 0.02) ( ) –10 ≈ ≈ ≈ Write.

Notes – Compound Interest Formula and Pe rt With Logs Remember, the formula for compound interest is: A = P(1 + (r/n)) (n*t) with A = Amount earned, P.

TEST TOMORROW 3/1/ NON-CALCULATOR MULTIPLE CHOICE 15-FREE RESPONSE QUESTIONS Unit 2 review.

Students will be able to: Use multiplication properties of exponents to evaluate and simplify expressions. Objective 8.1.

1.Simplify: 2. Simplify: 3.Simplify: 4.Simplify: 5. Solve for x: Warmup

MATH III – Exponential and Logarithmic Functions Exponential Growth and Decay.

Evaluate the following expressions using the calculator. No decimals! 1. (729) (5/6) (4/3) 3. ( 4  1296) 3 4. ( 5  1024) 2 Use the rules of exponents.

Exponential Functions Chapter 10, Sections 1 and 6.

February 9, 2012 At the end of today, you will be able to solve exponential functions. Warm-up: Evaluate without a calculator 1.arcsin HW 3.1b:

Warm-Up Exercises Evaluate the expression without using a calculator. ANSWER –1 ANSWER –3 2.–

Warm Up  Complete the Grok Activity on the back of your homework (the one with people at the top)

8.2 Interest Equations Key Q-How is an exponential function used to find interest? These are all money problems so you should have two decimal places.

Section 6-2 Day 1 Apply Properties of Rational Exponents.

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

Graphing $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $300 $ 200 $ 400.

Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and.

Warmup 3-24 Simplify. Show work! Solve for x. Show work! 4. 5.

7.1 nth roots and rational Exponents

Warmup Convert to radical form: 2. Convert to rational form:

Warmup Convert to radical form: 2. Convert to rational form:

Notes Over 8.3 Simplifying Natural Base Expressions

7.4 Rational Exponents.

Simplifying Numerical Expressions

Logarithmic Functions

Presentation transcript:

Warmup 11-16 Simplify: 2. Simplify: Simplify :

Review for Test Unit 5A Evaluate the following expressions using the calculator. No decimals! 1. (-1024)(2/5) 2. 625(3/4) 3. (3-216)5 4. (664)7 Use the rules of exponents to simplify. Show work!(treat “e” just like “x” in these problems) 5. (8e-5)-2 6. (12e7) (3e4) 7. 15e5 27e8 8. 36e-8 9. 9(e5)4 63e-2 39(e-7)-5 10. (x(1/5)  x(1/2))4 11. (x(2/5))(3/4) Simplify. Show work! 12. (60x9y6) `13. 3 (128x4y11)

Review for Test Unit 5A Simplify completely. Show work! 14. (121x8y2) 15. 9(4)(2/3) + 17(4)(2/3) 16. 4 (112x10y4) 17. 75x5y9z13 147x11y5z 18. 3 40x6y4z8 19. 4 162x3y14z10 375x9y16z2 512x7y2z2 20 30 21. -4 46 512 For #22-25, tell whether each equation given is an example of exponential growth or decay. 22. y = -ex+2 – 5 23. y = e-x-3 + 4 24. Y = -e-x+6 + 7 25. y = ex-1 - 2

Review for Test Unit 5A Solve for x. Show work! 83x-2 = (1/16)-x-24 27. 364x-5 = 62x+8 815x-8 = (1/9)2x-32 29. 49x-42 - 74 = -10 76x-16 + 92 = 141 31. Tim needs $11200 in 6 years to help pay for college. He is Investing some money at 5.75% interest compounded continuously. How much does Tim need to invest now to reach his goal in 6 years? Tammy is investing $7500 in an account earning 6% interest, compounded monthly. How much will she have in the account at the end of 4 years? 33. Joan is investing $2600 in an account earning 4.5% interest, compounded weekly. How much would she have earned in 3 years? James is investing $9600 in an account earning 4% interest, compounded continuously. How much will he have in the account in 7 years?

Review for Test – Unit 5A For #1-6, determine whether each equation is an example of exponential growth, or decay. Then, list the Domain, Range and Asymptote for each one. 1. y = (3)x + 2 2. y = -(5)x-3 Domain: Domain: Range: Range: Asymptote: Asymptote: Growth/Decay: Growth/Decay: 3. y = (1/4)x+4 4. y = -(1/3)x-5 + 3 Domain: Domain: 5. y = 2(1/5)x + 7 6. y = 4(2)x+1 - 4 Domain: Domain: Growth/Decay: Growth/Decay Solve for x. Show work! 7. 2(x – 8)3/2 + 12 = 28 8. 3(2x + 10)4/3 – 16 = 752 9. 4(3x – 21)2/5 + 27 = 63 10. 5(6x + 12)3/4 – 14 = 121 11. 7(5x – 45)5/2 + 64 = 21939

Convert the following radical expressions to rational form. Review for Unit 5A Convert the following radical expressions to rational form. (475) 5 2. (3-29)2 (38)7 4. 1 (532) Convert the following rational expressions to radical form. (72) (3/4) 6. (-21)(5/3) (13)(-1/4) 8. (31x)(-4/3) Evaluate the following expressions using the calculator. No decimals! 27(5/3) 10. 81(3/4) (6729)5 12. (3-125)4 Use the rules of exponents to simplify. Show work!(treat “e” just like “x” in these problems) 13. (2e4)5 14. (7e3) (5e6) 15. 16e7 24e11

Review for Unit 5A Use the rules of exponents to simplify. Show work!(treat “e” just like “x” in these problems) 21e-2 17. 3(e-4)-3 35e-5 14(e2)3 18. (x(2/5)  x(1/3))3 19. (x(1/4))(2/3) Simplify. Show work! (80x3y4) 21. 3 (108x7y8) 4 (405x8y15) 23. 3 24x6y11z4 81x9y5z 24. 4 32x5y7z2 25. 8 162xy15z22 3 6 -12 5 7