1. Today’s Agenda Fill in 3.1 Notes.
They are on the desk, please take one.
Turn in completed Test review (on desk NEXT TO red bin) from Friday (only if it is TOTALLY finished). Will not take it later today or tomorrow. Today only.

2. Section 3.1 Exponential Functions

3. Introduction
Just browsing? Take your time. Researchers know, to the dollar, the average amount the typical consumer spends per minute at the shopping mall. And the longer you stay, the more you spend. So if you say you’re just browsing, that’s fine with the mall merchants. Browsing is time and, as show in the graph, time is money.
How is the data growing?
Linearly? Quadratically? Exponentially?
Why do you think this way?

4. Intro Cont.
The function that we get from the data is _f (x) = 42.2(1.56)x_ where is the average amount spent, in dollars, at a shopping mall after x hours. How this is function different from the polynomials we looked at?
As you can see this function is an exponential function. Mainly because x is the exponent. Many real-life situation, including population growth, growth of epidemics (sickness) radioactive decay, and other changes that involve rapid decrease/increase use exponential functions.

6. Example 1

7. Example 2

8. Graphing Exponential Functions
Domain Range
Y-Intercept
Increasing Decreasing
Asymptotes
Inverse

9. Example 3
Domain
Range
Y-Intercept
Increasing Decreasing
Asymptotes
Inverse

10. Example 3
Domain
Range
Y-Intercept
Increasing Decreasing
Asymptotes
Inverse

12. Transformations of Exponential Functions

14. Up 3 Example 4 Domain g(x) Domain f(x) (-∞, ∞) (-∞, ∞) Range g(x)
Range f(x)
(-∞, ∞)
(-∞, ∞)
(0, ∞)
(3, ∞)

15. Right 2 Example 5 Domain g(x) Domain f(x) (-∞, ∞) (-∞, ∞) Range g(x)
Range f(x)
(-∞, ∞)
(-∞, ∞)
(0, ∞)
(0, ∞)

16. Example 6 Domain g(x) Domain f(x) (-∞, ∞) (-∞, ∞) Range g(x)
Stretch by 2
Reflect over y-axis
Domain g(x)
Range g(x)
Domain f(x)
Range f(x)
(-∞, ∞)
(-∞, ∞)
(0, ∞)
(0, ∞)

17. The Natural Base e

20. Example 7

21. Compound Interest

22. Compound Interest

23. Continuous Compounding

24. n = nothing because it is continuous
Example 8
n = 2
n = 4
n = 12
n = nothing because it is continuous
So we use Pe r t

25. (a)
(b)
(c)
(d)
(b)

26. (a)
(b)
(c)
(d)
(c)