1. Exponential Growth & Decay

2. I will Write and graph exponential growth models
Write and graph exponential decay models

3. Exponential Growth Model
y = A(1 + r)t
y: amount now
A: initial amount
(1+r): growth factor
r: growth rate as a decimal
t: time

4. Example
y =A(1 + r)t
y =0.06( )t
y =0.06(1.10)t
10% = .10

5. Your Turn
v =A(1 + r)t
v =50,000( )t
v =50,000(1.02)t
2% = .02

6. Example y =A(1 + r)t y =500(1.08)6 y =500(1 + .08)t y =500(1.08)t
8% = .08

7. Your Turn y =A(1 + r)t y = 750(1.06)10 y =750(1 + .06)t y ≈ $1,343
6% = .06

8. Write a Growth Model Given Growth FACTOR
y =A(1 + r)t
y =20(3)t
y =20(3)5
y =4,860
Mice
3 = (1 + r)

9. Write a Growth Model Given Growth FACTOR
y =A(1 + r)t
y =30(2)t
y =30(2)6
y =1,920
rabbits
2 = (1 + r)

10. Graph Exponential Growth Models
Large Growth Rate

11. Graph Exponential Growth Models
Small Growth Rate

12. Exponential Decay Model
y = A(1 - r)t
y: amount now
A: initial amount
(1-r): decay factor
r: decay rate as a decimal
t: time

13. Write, Use, & Graph Exponential Decay Models
y =A(1 - r)t
y =16,000( )t
y =16,000(.88)t
12% = .12
y = 16,000(.88)8 y ≈ $5,754.15

14. Your Turn y =A(1 - r)t y =24,000(1 - .10)t y =24,000(.90)t 10% = .10
y = 24,000(.90)6 y ≈ $12,754.58

15. Compare Growth & Decay Graphs

16. Compare Growth & Decay Graphs
2 = Growth Factor
Growth
1.1= Growth Factor
(1+r) > 1
2 > 1
(1-r) < 1
0< 0.5 < 1
Decay
0.5 = Decay Factor
(1-r) < 1
0< 0.2 < 1
(1+r) > 1
1.1 > 1
Decay
0.2 = Decay Factor