1. Section 1.2 Exponential Functions

2. Behavior of Functions Increasing Decreasing Constant Concave Up
Concave Down
Examples: y = x, y = x3, y = ex

3. Patterns of Growth Compare the following statements
The population of deer in Wyoming is increasing by 2500 deer per year
The population of deer in Wyoming is increasing by 4% per year
The value of a car decreases by $1000 per year
The value of a car decreases by 12% per year

4. Patterns of Growth LINEAR GROWTH can be described by:
The terms additive and arithmetic The same amount is added to each successive stage (common difference) A linear function, whose graph is a straight line Constant rate of change
EXPONENTIAL GROWTH can be described by:
The terms multiplicative and geometric The same factor is multiplied by each successive stage (common ratio) An exponential function, whose graph is a curved

5. What can you say about the Domain? Range? Intercepts? Behavior?
Exponential Growth
Graph: y1= 2x, y2= 4x
What can you say about the Domain? Range? Intercepts? Behavior?

6. End Behavior

7. Graph: y1= (¼)x, y2=(½)x , y3=(0.99)x
Exponential Decay
Graph: y1= (¼)x, y2=(½)x , y3=(0.99)x
What can you say about the Domain? Range? Intercepts? Behavior?

8. End Behavior

9. General Exponential Function base e e = 2.71828...
Just a note…
The number e is defined as the number aaaaaaaaapproaches as n ∞
From this we get the general exponential function
Where k is the continuous growth rate

10. An alternative form using the natural base is f(t) = aekt
An exponential function Q = f(t) has the formula f(t) = abt, b > 0, where a is the initial value of Q (at t = 0) and b, the base related to the rate at which it grows or decays.
Note that it is called an exponential function because the input, t, is in the exponent
b = (1 + r) where r is the growth or decay rate
An alternative form using the natural base is f(t) = aekt
In this form b = ek

11. The half-life of a substance is the amount of time it takes for a decreasing exponential function to decay to half of its initial value
The half-life of iodine-123 is about 13 hours. You begin with 100 grams of iodine-123. Write an equation that gives the amount of iodine remaining after t hours
Doubling time is the amount of time it takes for an increasing exponential function to grow to twice its previous level
A bank account doubles in value every 21 years. Write a formula that gives the balance of the account after t years if $500 is deposited initially. What is the annual rate of the account?

12. Patterns of Growth Create a model for the following statements
The population of deer in Wyoming is increasing by 2500 deer per year
The population of deer in Wyoming is increasing by 4% per year
The value of a car decreases by $1000 per year
The value of a car decreases by 12% per year