1. Graphing Exponentials and Logs
Day 2
Graphing Exponentials and Logs

2. 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.

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

4. initial amount growth factor (1+r)
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?

5. 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?

6. Exponential Decay: y = a(1-r)t
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.

7. More Decay…..
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.

8. 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.

9. Graphing Exponential Decay
y = 24(1/3)x
Horizontal Asymptote
Domain
Range x y -3 -2 -1 1 2 3

10. Graphing Exponential Decay
y = 100(0.1)x
Horizontal asymptote
Domain
Range x y -3 -2 -1 1 2 3

11. Graph and give asymptote, domain and range.

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

13. Translating y = abx
y =2(3)x-1 + 1
y = -3(4)x+1 +2

14. Homework
Pg. 296 (1-14, 29-34)