1. Homework Questions!

2. Exploring Exponential Models
Unit 3
Exploring Exponential Models

3. An exponential function is a function with the general form of:
y = abx
where x is a real number,
a ≠ 0, b > 0, and b ≠ 1.

4. Graphing Exponential Equations
y = 2x x y -3 -2 -1 1 2 3

5. EXPONENTIAL GROWTH y = a • bx time initial amount growth factor (1+r)
Ex. The population of the US in 1994 was about 260
million with an average annual rate of increase
of about 0.7%.
1. Write a function to model this population.
2. What was the population in 2006?

6. Modeling growth The bear population increases at a rate
of 2% per year. There are 1573 bears this year. Write a function that models the bear population. How many bears will there be in 10 years?

7. Exponential Decay
y = a(1-r)t
Ex. 1. Suppose you want to buy a used car that costs $11,800. The expected depreciation of the car is 20% per year. Estimate the depreciated value of the car after 6 years.

8. More Decay…..
Ex. 2. The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 animals in the habitat. Write the equation.

9. Ex: Analyzing a Function
Without graphing, determine whether the function y = 14(0.95)x represents exponential growth or exponential decay.
Without graphing, determine whether the function y = 0.2(5)x represents exponential growth or exponential decay.

10. An asymptote is a line that a graph approaches as x or y increases in absolute value.

11. Ex: Graphing Exponential Decay
y = 24(1/3)x
Identify.
Horizontal Asymptote
Domain
Range x y -3 -2 -1 1 2 3

12. Example 5b Graphing Exponential Decay
y = 100(0.1)x
Identify.
Horizontal asymptote
Domain
Range x y -3 -2 -1 1 2 3

13. Example 2 Translating y = abx
y =8(1/2)x
y = 8(1/2)x+2 +3

14. Example 2b Translating y = abx
y =2(3)x-1 + 1
y = -3(4)x+1 +2

15. Half-life! A = A0(1/2) What does that mean?
The half-life is the amount of time it takes for half of the atoms in a sample to decay.
* t
A = A0(1/2)
Half life

16. Example 3 Real World Connection
A hospital prepares a 100-mg supply of technetium-99mg which has a half-life of 6 hours. Write an exponential function to find the amount of technetium-99mg that remains after 75 hours.

17. Another Half-Life?
Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. Write an exponential decay function for a 90-mg sample. Use the function to find the amount remaining after 6 days.

18. Classwork/homework
Worksheet