UNIT 5 Exponential and Logarithmic Functions OH YEAH

UNIT 5 Exponential and Logarithmic Functions! OH YEAH!

Unit Essential Question • How are exponential and logarithmic functions related, and how can they be represented graphically?

LESSON 5. 1 Exponential Functions

Lesson Essential Question (LEQ) • What is an exponential function and how can they be represented graphically?

Solving Exponential Equations •

Sketching Graphs •

Even More Graphs! •

Real World Applications: • Compound Interest • Decay/Growth • Half-Life • Bloodstream • Appreciation/Depreciation • Inflation • Epidemics • Many more…

Homework: • Page 334 -335 • #’s 1, 3, 5, 7, 9, 13, 15, 17, 21, 30, 31 a, 33 a, 35

Bell Work: •

Compound Interest: •

Examples: • Ex: If you invested $2, 000 dollars 10 years ago at 4. 5% that was compounded quarterly, what would be the value of that investment today? • Ex: Mr. Kelsey needs to have $2, 000 by the time he retires in 33 years. He plans to invest in a money market account that will return 5. 25% per year. How much money will he need to invest right now to reach his goal?

Classwork/Homework: • Pages 335 -336 • #’s 37 – 42, 45 -48

Bell Work: • The current average cost of gasoline per gallon in PA is $2. 79 and has been increasing at an average inflation rate of 3. 75% per year. If this pattern holds true, what will be the cost of gas in 30 years?

LESSON 5. 2 The Natural Exponential Function

LESSON ESSENTIAL QUESTION • What is the natural exponential function and how can it be used?

Important: •

Continuously Compounded Interest •

Law of Growth/Decay Formula •

Homework: • Pages 345 -346 • #’s 5 – 15 odds, 19 -31 odds

Bell Work: •

Small Quiz Monday: • You will need to know for tomorrow: • Solve exponential equations • Compound Interest Formula • Word Problems • Solve natural exponential equations • Continuously Compounded Interest • Growth/Decay Formula • Word Problems! • WORD PROBLEMS!!!!!

Classwork/Homework: • Pages 345 -347 #’s 6, 8, 12, 14, 20, 22, 24, 26 a, 28, 32 • This assignment will be collected!

Bell Work: •

Examples: •

Bell Work: • 1) Colten begins a new job working for $15. 25 an hour. Every year he will get a annual 3% cost of living raise. If he works at this same job for 30 years, what will be his hourly wage?

LESSON 5. 3 Logarithmic Functions

Lesson Essential Question: • How are logarithmic functions related to exponential functions and what are the different properties of logarithms?

Logarithm •

Graphs of Logarithms •

Rewriting Logarithms •

Rewriting Exponents •

Simplifying Logarithms •

Bell Work: •

Properties of Logarithms • Page 350 Blue Table • Remember These Properties!!!!!

Solving Logarithmic Equations •

Common Logarithm •

NATURAL LOGARITHMS!!!!! •

Blue Table on Page 356 •

Homework: • Pages 359 – 360 • #’s 2, 4, 10, 12, 14, 16 – 32 evens

Bell Work: • Be ready to ask questions on the homework! • If not, begin working on the following assignment which is due Monday! (It will be collected!) • Pages 359 – 360 #’s 1, 3, 13 – 31 odds

Bell Work: •

Graphing Logarithms •

Shifting/Reflecting • The graphs of logarithms behave just like any other functions. • Lets sketch the graphs of some functions that will shift and/or reflect.

Class Examples: • Pages 362 – 363 #’s 52, 54, 60, 66, 70

Homework: • Page 360 #’s 51 - 69 odds

Bell Work: • The current population of Bloomsburg in 2015 is approximately 12, 000. It is projected to grow continuously in the future at a rate of 1. 85%. How long will it take for the population of Bloomsburg to double in size?

LESSON 5. 4 Properties of Logarithms

Lesson Essential Question • What are the different properties of logarithms and how are they used when simplifying exponential and/or logarithmic expressions?

Three More Properties of Logarithms • ORANGE TABLE ON PAGE 364 • These properties hold true for the common logarithm and the natural logarithm. (Blue Table Page 365)

Examples: •

Examples: •

Solving Logarithmic Equations: •

Homework: • Page 370 #’s 1 -33 odds

Bell Work: • Get out your homework from last night: • Page 370 1 -33 odds • Be ready to ask questions!

Quiz Tomorrow: • LOGARITHMS! • (remember that to answer some logarithmic problems you need to know how to change to exponential form) • On the quiz: • Solving Logarithms • Word Problems • Properties of Logarithms • WORD PROBLEMS!!!

Class Work: • Pages 370 – 371 #’s 6, 8, 10, 12, 14, 18, 20, 22, 26, 34, 51, 52, 53, 54, 56

Bell Work: •

LESSON 5. 5 Exponential and Logarithmic Equations

Lesson Essential Question • How can we change the bases of logarithmic and exponential functions, and how do we use the special base formulas?

Example: •

Change of Base Formula: •

Examples: •

Solving an Exponential Equation •

Homework: • Pages 381 -382 #’s 1 -31 odds only

Bell Work: •

Solving a Logarithmic Equation: •

Finding an inverse function: •

Example using the Logistic Curve •

Class Work/Homework: • Pages 381 -383 #’s 33 – 39 odds 49, 53 b, 54, 55, 56 a, 56 c, 57 • If you need extra practice, try the evens (2 – 40)

Unit Test • Thursday and Friday we will be having our Unit 5 Test on exponential and logarithmic functions. • Here is a group of review exercises to try: • Pages 385 – 387 • #’s 17 – 40, 45 and 46 (just find the inverse), • 47 – 55, 58, 61, 62, 66, 67