1. Work on Exp/Logs
The following slides will help you to review the topic of exponential and logarithmic functions from College Algebra.
Also, I am introducing the rules for differentiating these functions (for base e) in preparation for Monday’s class.

2. Exponential and Logarithmic Functions
Recall the basic forms for
An exponential function with base b
A logarithmic function with base b

3. Base e e is an irrational number An exponential function with base e
A logarithmic function with base e

4. Exponential and Logarithmic Forms of an EQ
An exponential equation with base b can be rewritten as a logarithmic equation as follows:
SAY: b to the x power = c
SAY: log base b of c = x
Base = b
Exponent = the logarithm = x

5. Exponential and Logarithmic Forms of an EQ
Practice changing forms:
Exponential form Logarithmic form

6. Exponential and Logarithmic Forms of an EQ
Practice changing forms:
Exponential form Logarithmic form

7. An Exponential Application
An application with the natural exponential function involved interest compounded continuously:
where A = amount, P = principal,
r = rate, and t = time in years

8. Example
Suppose we have $10,000 to invest and we find a bank that will compound continuously at a rate of 2.5%. How long will it take for our money will double?
Do you remember how to do this? See next slide…

9. Example
Use:
P = $10,000 A = $20,000
r = 0.025, solve for t

10. Now solve the equation By hand: Divide by 10000:
Change to a logarithmic
equation
Divide by 0.025:
Get a calculator
approximation:

11. It is its OWN derivative!
To differentiate:
Given a function of the form
we find that its derivative is
It is its OWN derivative!

12. How does this work if a = e?
In general:
Given a function of the form
we find that its derivative is
How does this work if a = e?

13. An example: Given a function of the form its derivative is given as
IN WORDS: we repeat the exponential function then multiply by the derivative of the exponent

14. Next rule:
Given a function of the form
we find that its derivative is

15. Next rule:
Given a function of the form
we find that its derivative is

16. Let’s see the chain rule here
Given the function
its derivative is given as

17. In words: reciprocal derivative of the variable x of the variable
expression expression