1. Name:__________ warm-up 7-3 Solve 4 2x = 16 3x – 1 Solve 8 x – 1 = 2 x + 9 Solve 5 2x – 7 < 125 Solve

2. A money market account pays 5.3% interest compounded quarterly. What will be the balance in the account after 5 years if $12,000 is invested Charlie borrowed $125,000 for his small business at a rate of 3.9% compounded annually for 30 years. At the end of the loan, how much will he have actually paid for the loan?

3. Details of the Day EQ: How do radical functions model real-world problems and their solutions? How are expressions involving radicals and exponents related? I will be able to… Activities: Warm-up Review homework Notes: 7-3 Logarithmic and Logarithmic functions Class work/ HW Vocabulary: logarithmic function logarithm http://www.purplemath.com/modules/logs.h tm.. Evaluate logarithmic expressions. Graph logarithmic functions.

4. 7-3 Logarithm and Logarithmic Functions

5. A Quick Review Solve 4 2x = 16 3x – 1 Solve 8 x – 1 = 2 x + 9 Solve 5 2x – 7 < 125 Solve

6. A Quick Review A money market account pays 5.3% interest compounded quarterly. What will be the balance in the account after 5 years if $12,000 is invested Charlie borrowed $125,000 for his small business at a rate of 3.9% compounded annually for 30 years. At the end of the loan, how much will he have actually paid for the loan?

7. Notes and examples Write log 3 9 = 2 in exponential form. B. Write in exponential form.

8. Notes and examples What is log 2 8 = 3 written in exponential form? What is 3 4 = 81 written in logarithmic form? What is –2 written in exponential form? B. Write in logarithmic form.

9. Notes and examples What is written in logarithmic form? Evaluate log 3 243 Evaluate log 10 1000

10. Notes and examples

11. Graph the function f(x) = log 3 x Graph the function

12. Notes and examples Graph the function f(x) = log 5 xGraph the function

13. Notes and examples ● : The graph is compressed vertically. ● h = 0: There is no horizontal shift. ● k = –1: The graph is translated 1 unit down.

14. Notes and examples ● |a| = 4: The graph is stretched vertically. ● h = –2: The graph is translated 2 units to the left. ● k = 0: There is no vertical shift.

15. Notes and examples

16. A. AIR PRESSURE At Earth’s surface, the air pressure is defined as 1 atmosphere. Pressure decreases by about 20% for each mile of altitude. Atmospheric pressure can be modeled by P = 0.8 x, where x measures altitude in miles. Find the atmospheric pressure in atmospheres at an altitude of 8 miles.

17. Notes and examples B. AIR PRESSURE At Earth’s surface, the air pressure is defined as 1 atmosphere. Pressure decreases by about 20% for each mile of altitude. Atmospheric pressure can be modeled by P = 0.8 x, where x measures altitude in miles. Write an equation for the inverse of the function.

18. Notes and examples A. AIR PRESSURE The air pressure of a car tire is 44 lbs/in 2. The pressure decreases gradually by about 1% for each trip of 50 miles driven. The air pressure can be modeled by P = 44(0.99 x ), where x measures the number of 50-mile trips. Find the air pressure in pounds per square inch after driving 350 miles.

19. Notes and examples B. AIR PRESSURE The air pressure of a car tire is 44 lbs/in 2. The pressure decreases gradually by about 1% for each trip of 50 miles driven. The air pressure can be modeled by P = 44(0.99 x ), where x measures the number of 50-mile trips. Write an equation for the inverse of the function.