1. Warm Up
A calculator factory has increased the amount of calculators produced from 900 to 1300 calculators. What is the percentage of increase?
Nike sales increased from $85 million dollars in to $107 million in Calculate the change, the percentage change, and the average rate of change in Nike’s sales from 2010 through 2012.

2. Homework Review
After 30 baseball games, A-Rod had 25 hits. If after 100 games he had 80 hits, what is his average hits per baseball game.
A plane left Chicago at 8:00 A.M. At 1: P.M., the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip?
A teacher weighed 145 lbs in 1986 and weighs 190 lbs in What was the average rate of change in weight?
Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the average rate of change of money in his savings account per week?
The Gap saw its sales rise from $1934 million dollars in 1991 to $5284 million in Calculate the change, the percentage change, and the average rate of change in the Gap’s sales from 1991 through 1997. 2

3. Evaluating Exponentials and Logarithms

4. Objective
SWBAT evaluate exponential and logarithmic expressions

5. Vocabulary Exponential Function Logarithmic Function Natural Base
Common Logarithm
For x > 0 and 0 < a ≠ 1, y = loga x if and only if x = ay
A base of e or approximately 2.718
A logarithm with a base of 10

6. Evaluating Exponents
With polynomial and rational functions we only look at exponents that have integer and rational values, in exponential functions we will expand to look at irrational values in the exponent as well
Any exponential function can be evaluated in the calculator

7. Example
1. Evaluate when x = 5/7

8. Practice Evaluate when x = -3.1 Evaluate when x = π

9. Base e
In many applications the most convenient choice for a base is the irrational value e
2ND ÷
e is approximately equal to and is called the natural base
we can evaluate natural base exponential functions in our calculator the same way we would evaluate any other exponential function

10. Example
1. Evaluate when x = -0.3

11. Practice Evaluate when x = -2 Evaluate when x = -1

12. Evaluating Logarithms
A logarithmic function is the inverse of an exponential function
This means that loga x is the exponent to which a must be raised to obtain x
By this definition, we can’t take the logarithm of a negative number
Only certain logarithms can be computed in the calculator

13. Common Logarithms
Logarithms with the base 10 are called common logarithms and abbreviated as log
Common logarithms can be computed in the calculator
Example: log(12)

14. Change of Base
If you want to compute logarithms with bases other than 10 in the calculator you have to use the change-of-base formula
Change-of-Base Formula
loga x can be converted to a different base as follows.

15. Example
Evaluate log4 30

16. Example
2. Evaluate log2 14

17. Example
1. Evaluate f(x) = log4 x when x = 2

18. Practice Evaluate f(x) = log2 x when x = 32

19. Natural Logs The same natural base e exists for logarithmic functions
To evaluate natural logarithms we use the ln function in the calculator
Just as you can’t take the logarithm of a negative number, you can’t take the natural logarithm of a negative number

20. Example
1. Evaluate f(x) = ln x when x = 0.3

21. Practice Evaluate f(x) = ln x when x = 2